Jahn‐Teller‐Ordnung in Mangan(III)‐fluoridsulfaten. II. Phasenübergang und Verzwillingung bei K2[MnF3(SO4)] und 1D Magnetismus in Verbindungen A2[MnF3(SO4)] (A = K,NH4, Rb,Cs)

Jahn‐Teller Ordering in Manganese(III) Fluoride Sulfates. II. Phase Transition and Twinning of K₂[MnF₃(SO₄)] and 1D Magnetism in Compounds A₂[MnF₃(SO₄)] (A = K, NH₄, Rb, Cs) According to single‐crystal X‐ray investigations, K₂[MnF₃(SO₄)] crystallizes at low temperature, like the isostructural Rb, NH₄, and Cs analogues in space group P2₁/c, Z = 4, e.g. at 100 K with a = 7.197, b = 10.704, c = 8.427Å, β = 91.84°. Below about 300 K, the crystals are found to be [001] axis twins. Using a new integration method for area detector records, nearly complete intensity data could be gained allowing for structure refinements of similar quality as for untwinned crystals (e.g. at 100 K: wR₂ = 0.050, R = 0.020 for all reflections). With rising temperature, the monoclinic angle approaches continuously 90°. For an ordering parameter Δβ = β?90° a 2^nd‐order phase transition is observed with an exponent λ = 0.17. At the transition temperature of 280 K resulting from the fit, the monoclinic structure changes – with delay – to orthorhombic with the minimum super‐group Pnca, a = 7.243, b = 10.763, c = 8.457Å, R = 0.024, as found in an early structure determination at room temperature by Edwards 1971. In the chain‐like [MnF₃(SO₄)]^2? anions, manganese(III) is octahedrally coordinated by two trans‐terminal and two trans‐bridging fluorine ligands as well as by the O atoms of two trans‐bridging sulfate ligands. At low temperature, the octahedral elongation by the Jahn‐Teller effect alternates between a F–Mn–F and an O–Mn–O axis (antiferrodistortive ordering). All bridges are asymmetric. From about 320 K on they become symmetric. Due to 2D dynamical Jahn‐Teller effect all octahedra appear compressed. All compounds A₂[MnF₃(SO₄)] show 1D antiferromagnetism. The antiferrodistortive Jahn‐Teller order at low temperatures and the small bridge angles explain the much lower magnetic exchange energies and their inverse relation to the bridge angles as compared with other fluoromanganate(III) chain compounds with the usual ferrodistortive ordering.     

Structure and spectra of the molecules of manganese, iron, and cobalt trifluorides: A CCSD(T) study in the complete basis set

The coupled-cluster singles and doubles with perturbative triples (CCSD(T)) method in triple-, quadruple-, and quintuple-zeta basis sets with extrapolation to the complete basis set limit is used to analyze the properties of MnF₃, FeF₃, and CoF₃ molecules. The relative energies of low-lying electronic states are determined. The Jahn-Teller effect is investigated in the ground electronic state ⁵ E?? of the MnF₃ molecule and the first excited electronic state ⁵ E?? of the CoF₃ molecule. Geometric parameters, atomization enthalpies, vibrational frequencies, intensities in the infrared and Raman spectra are found with high accuracy. The assignment of the bands observed in the low-frequency region of the IR and Raman spectra of MnF₃ and CoF₃ molecules are revised.     

Jahn‐Teller‐Ordnung in pipzH2[Mn2F8], einem Fluoromanganat(III) mit neuer Schichtstruktur

Jahn‐Teller Ordering in pipzH₂[Mn₂F₈], a Fluoromanganate(III) with a New Layer Structure From a solution of (pipzH₂)[MnF₂(HPO₄)(H₂O)]·(H₂PO₄) in concentrated hydrofluoric acid the title compound could be crystallized and was characterized by X‐ray crystallography: monoclinic, space group P2₁/n, Z = 8, a = 13.275(1), 10.400(1), c = 14.928(1) Å, β = 112.337(8), R = 0.0265. The structure shows a new type of anionic layers [Mn₂F₈] built of dimers of edge‐sharing [MnF₆] octahedra linked via common vertices, alternating with layers of piperazinium(2+) cations. A dense network of hydrogen bonds N–H···F achieves a strong 3D interconnection. Strong elongation of the [MnF₆] octahedra is observed due to the Jahn‐Teller effect.The long axes show parallel (ferrodistortive) orientation within the dimers, but the ordering between the dimers is antiferrodistorive. A possible mechanism of formation is discussed on the basis of precursor structures.     

Cooperative Jahn–Teller distortion leading to the spin-1/2 uniform antiferromagnetic chains in triclinic perovskites AgCuF3 and NaCuF3

Polycrystalline samples of AgCuF₃, isostructural with NaCuF₃, were synthesized by solid state reaction and characterized by powder X-ray diffraction. The magnetic properties of AgCuF₃ and NaCuF₃ were examined by measuring their magnetic susceptibilities and evaluating their spin exchange interactions. The three-dimensional CuF₃ network of corner-sharing CuF₆ octahedra present in AgCuF₃ and NaCuF₃ shows a cooperative Jahn–Teller distortion such that their magnetic susceptibilities above 50 K are well described by an S = 1/2 Heisenberg uniform antiferromagnetic chain model with average spin exchange of J/k_B ≈ ?300 and ?180 K, respectively. The relative strengths of these interactions are well reproduced by spin dimer analysis based on tight-binding calculations, but not by mapping analysis based on first principles density functional calculations.     

Optical spectra of some octahedral transition metal fluorides as calculated by multiple scattering method

The electronic spectra of the octahedral clusters TiF^3?₆, CrF^3?₆, MnF^2?₆, NiF^2?₆, and NiF^4?₆ are calculated using the multiple-scattering model with statistical exchange. The agreement is satisfactory, indicating that this simple method can be used for detailed investigations of the electronic structure of transition metal complexes.     

Nonadiabatic theory of triatomics: Formalism for 1Πu/1Φg interaction,for electronic spin,and for 2Λ Renner–Teller effect

A recent theory of nonadiabatic effects in triatomic molecules is specialized to the four-state Renner–Teller and Jahn–Teller ¹Π_u/¹Φ_g interactions and is then generalized by including the electronic spin and by considering the ²Λ Renner–Teller effect.     

Fluorination of fluoro-cyclobutene with high-valency metal fluoride

Fluorinations of 1,4,4-trifluorocyclobutene and 3,3,4,4-tetrafluorocyclobutene using high-valency metal fluorides such as CoF₃, MnF₃, AgF₂, CeF₄ and KCoF₄, and elemental fluorine were examined. In these reactions with CoF₃ and MnF₃, vic-difluorination proceeded mainly. While, 1,4,4-trifluorocyclobutene yielded 3,3,4,4-tetrafluorocyclobutene, and 3,3,4,4-tetrafluorocyclobutene yielded 1,3,3,4,4-pentafluorocyclobutene mainly in the case of AgF₂. The further fluorinated products were increased under severer conditions. Also, the plausible reaction mechanism was suggested.     

Metal–Organic Perovskites: Synthesis,Structures, and Magnetic Properties of [C(NH2)3][MII(HCOO)3] (M=Mn,Fe, Co,Ni, Cu,and Zn; C(NH2)3= Guanidinium)

We report the synthesis, crystal structures, and spectral, thermal, and magnetic properties of a family of metal–organic perovskite ABX₃, [C(NH₂)₃][M^II(HCOO)₃], in which A=C(NH₂)₃ is guanidinium, B=M is a divalent metal ion (Mn, Fe, Co, Ni, Cu, or Zn), and X is the formate HCOO^?. The compounds could be synthesized by either diffusion or hydrothermal methods from water or water‐rich solutions depending on the metal. The five members (Mn, Fe, Co, Ni, and Zn) are isostructural and crystallize in the orthorhombic space group Pnna, while the Cu member in Pna2₁. In the perovskite structures, the octahedrally coordinated metal ions are connected by the anti–anti formate bridges, thus forming the anionic NaCl‐type [M(HCOO)₃]^? frameworks, with the guanidinium in the nearly cubic cavities of the frameworks. The Jahn–Teller effect of Cu²⁺ results in a distorted anionic Cu–formate framework that can be regarded as Cu–formate chains through short basal Cu? O bonds linked by the long axial Cu? O bonds. These materials show higher thermal stability than other metal–organic perovskite series of [AmineH][M(HCOO)₃] templated by the organic monoammonium cations (AmineH⁺) as a result of the stronger hydrogen bonding between guanidinium and the formate of the framework. A magnetic study revealed that the five magnetic members (except Zn) display spin‐canted antiferromagnetism, with a Néel temperature of 8.8 (Mn), 10.0 (Fe), 14.2 (Co), 34.2 (Ni), and 4.6 K (Cu). In addition to the general spin‐canted antiferromagnetism, the Fe compound shows two isothermal transformations (a spin‐flop and a spin‐flip to the paramagnetic phase) within 50 kOe. The Co member possesses quite a large canting angle. The Cu member is a magnetic system with low dimensional character and shows slow magnetic relaxation that probably results from the domain dynamics.     

An investigation of the electron density of a Jahn–Teller‐distorted CrII cation: the crystal structure and charge density of hexakis(acetonitrile‐κN)chromium(II) bis(tetraphenylborate) acetonitrile disolvate

In the crystal structure of the title homoleptic Cr^II complex, [Cr(CH₃CN)₆](C₂₄H₂₀B)₂·CH₃CN, the [Cr(CH₃CN)₆]²⁺ cation is a high‐spin d⁴ complex with strong static, rather than dynamic, Jahn–Teller distortion. The electron density of the cation was determined by single‐crystal X‐ray refinements using aspherical structure factors from wavefunction calculations. The detailed picture of the electronic density allowed us to assess the extent and directionality of the Jahn–Teller distortion of the Cr^II cation away from idealized octahedral symmetry. The topological analysis of the aspherical d‐electron density about the Cr^II cation showed that there are significant valence charge concentrations along the axial Cr—N axes. Likewise, there were significant valence charge depletions about the Cr^II cation along the equatorial Cr—N bonds. These charge concentrations are in accordance with a Jahn–Teller‐distorted six‐coordinate complex.     

Excited-State Distortions Promote the Photochemical 4π-Electrocyclizations of Fluorobenzenes via Machine Learning Accelerated Photodynamics Simulations

Benzene fluorination increases chemoselectivities for Dewar-benzenes via 4π-disrotatory electrocyclization. However, the origin of the chemo- and regioselectivities of fluorobenzenes remains unexplained because of the experimental limitations in resolving the excited-state structures on ultrafast timescales. The computational cost of multiconfigurational nonadiabatic molecular dynamics simulations is also currently cost-prohibitive. We now provide high-fidelity structural information and reaction outcome predictions with machine-learning-accelerated photodynamics simulations of a series of fluorobenzenes, C₆F_6-nH_n, n=0–3, to study their S₁→S₀ decay in 4 ns. We trained neural networks with XMS-CASPT2(6,7)/aug-cc-pVDZ calculations, which reproduced the S₁ absorption features with mean absolute errors of 0.04 eV (<2 nm). The predicted nonradiative decay constants for C₆F₄H₂, C₆F₆, C₆F₃H₃, and C₆F₅H are 116, 60, 28, and 12 ps, respectively, in broad qualitative agreement with the experiments. Our calculations show that a pseudo Jahn–Teller distortion of fluorinated benzenes leads to an S₁ local-minimum region that extends the excited-state lifetimes of fluorobenzenes. The pseudo Jahn–Teller distortions reduce when fluorination decreases. Our analysis of the S₁ dynamics shows that the pseudo-Jahn–Teller distortions promote an excited-state cis-trans isomerization of a π_C-C bond. We characterized the surface hopping points from our NAMD simulations and identified instantaneous nuclear momentum as a factor that promotes the electrocyclizations.     

Solution chemistry of cobalt in liquid hydrogen fluoride

Cobalt(II) fluoride dissolves in HF in the presence of excess BF₃ or AsF₅: solid adducts are isolable from these solutions. Insoluble CoF₃ decomposes to cobalt(II) under the same conditions. The CoF^3?₆ is solvolysed by HF except in the presence of excess F^?. Cs₂CoF₆ is soluble in HF but the solutions decompose above 10°C yielding F₂; such solutions are powerful fluorinating agents and convert MnF₃ to MnF^2?₆ and Xe to XeF₂.     

Electronic Structure Manipulation of the Mott Insulator RuCl3 via Single-Crystal to Single-Crystal Topotactic Transformation

The core task for Mott insulators includes how rigid distributions of electrons evolve and how these induce exotic physical phenomena. However, it is highly challenging to chemically dope Mott insulators to tune properties. Herein, we report how to tailor electronic structures of the honeycomb Mott insulator RuCl₃ employing a facile and reversible single-crystal to single-crystal intercalation process. The resulting product (NH₄)_0.5RuCl₃⋅1.5 H₂O forms a new hybrid superlattice of alternating RuCl₃ monolayers with NH₄⁺ and H₂O molecules. Its manipulated electronic structure markedly shrinks the Mott–Hubbard gap from 1.2 to 0.7 eV. Its electrical conductivity increases by more than 10³ folds. This arises from concurrently enhanced carrier concentration and mobility in contrary to the general physics rule of their inverse proportionality. We show topotactic and topochemical intercalation chemistry to control Mott insulators, escalating the prospect of discovering exotic physical phenomena.     

The first‐row transition‐metal series of tris(ethylenediamine) diacetate complexes [M(en)3](OAc)2 (M is Mn,Fe, Co,Ni, Cu,and Zn)

The crystal structures of the first‐row transition‐metal series of tris(ethylenediamine‐κ²N ,N ′)metal(II) diacetate, [M (C₂H₈N₂)₃](CH₃CO₂)₂, with M = Mn, Fe, Co, Ni, Cu, and Zn, are reported. The complexes are all isostructural, crystallizing in a centrosymmetric triclinic cell and possessing an asymmetric unit composed of one [M (en)₃]²⁺ cation and two symmetrically independent acetate anions. In the unit cell, the two complex cations are inversion‐generated enantiomers, possessing the energetically favoured Δ(λλλ) and Λ(δδδ) configurations. The complex cations and acetate anions combine through a series of N—H…O hydrogen bonds to generate a three‐dimensional network in the crystals. The other notable feature of the series is a significant Jahn–Teller distortion for the d ⁹ Cu²⁺ complex.     

One-dimensional end-to-end azide-bridged Mn(III) complexes incorporating alkali metal ions: slow magnetic relaxations and metamagnetism

Three azide‐bridged Mn^III chains [Mn(3‐MeOsalpn)(N₃)] ? 0.5 AClO₄ (A=Na ( 1 ), K ( 2 ), Rb ( 3 ); 3‐MeOsalpn=N,N′‐propylenebis(3‐methoxysalicylideneiminato) dianion) incorporating alkali metal ions and perchlorate anions were systematically synthesized. The overall structure can be described as a one‐dimensional chain bridged by end‐to‐end azide ligands, although spatial arrangements of Jahn–Teller axes of Mn in 1 and 2 are different from that in 3 . Relying on the alkali metal ions, magnetic properties are varied from a two‐step phase transition ( 1 ) to metamagnetic transitions ( 2 and 3 ). In this system, spin canting definitely plays a central role in giving rise to the apparent slow magnetic relaxations in 1 and 2 because application of a high external magnetic field tends to destroy single‐chain magnet (SCM) properties. Despite the existence of a long‐range antiferromagnetic order at T_N, slow magnetic relaxation is notably observed in 2 , which likely emanates from the operative spin canting below T_N.     

Magneto-structural correlation in Cu(NH3)2Ag2(CN)4. Crystal structure,magnetic and thermodynamic properties of an S = 1/2 low-dimensional Heisenberg antiferromagnet

Crystal structure, thermodynamic properties and electron spin resonance spectra of Cu(NH₃)₂Ag₂(CN)₄ have been studied. The structure of the studied compound consists of interpenetrating wave-shaped two-dimensional (2d) arrays, in which CuN₄N₂ octahedra axially elongated due to the Jahn–Teller effect are linked by diamagnetic [Ag(CN)₂]⁻ anions forming a square lattice. Although the susceptibility and specific heat data confirm the existence of short-range order at about 2 K, quantitative analysis of the experimental data reveals that the magnetic behavior differs from that of the crystal structure expected for 2d Heisenberg magnet on the square lattice. Structural features responsible for the observed difference are discussed. In addition, it is suggested, that additional degrees of freedom contribute to the thermodynamic equilibrium properties in the millikelvin temperature range.     

Relativity and the Jahn–Teller,Berry pseudorotations of TBP clusters: group theory,spin–orbit and combinatorial nuclear spin statistics of TBP Desargues–Levi isomerization graph

Jahn–Teller and Berry pseudorotations in transition metal and main group clusters such as Hf₅, Ta₅, W₅ and Bi₅ are interesting because of the competition between relativistic effects and pseudorotations. Topological representations of various isomerization pathways arising from the Berry pseudorotation of pentamers constitute the edges of the Desargues–Levi graph. We have computed the combinatorics for multinomial colorings of the vertices, edges and 10-faces of the Desargues–Levi isomerization graph for all irreducible representations and the nuclear spin statistics of spin-7/2 ¹⁸¹Ta₅ as well as the TBP composite cluster particles. Topological insights into Jahn–Teller and Berry pseudorotations and relativistic effects are provided.     

Synthesis and structures of three heterobimetallic compounds based on a new ferrocenyl pyridine ligand

The reactions of 2-PAMF with metal perchlorates [2-PAMF = (2-pyridylmethylamino)carbonylferrocene] yielded three coordination compounds, M(2-PAMF)₂(CH₃CH₂OH)₂(ClO₄)₂ (M = Co 1, Zn 2, and Cu 3), which were characterized by single crystal X-ray diffraction and IR spectroscopy. Compounds 1 and 2 have similar structures with six-coordinate metals in octahedral geometries. The CuII in 3 possesses a severely distorted octahedral geometry due to Jahn–Teller distortion. Adjacent molecules in the three compounds were linked by intermolecular hydrogen bonds to form a 1-D supramolecular chain.     

Doppelkettenstruktur von (pipzH2)[MnF2(HPO4)(H2O)](H2PO4)

By adding piperazine to a hydrofluoric and phosphoric acid solution of Manganese(III) fluoride, the fluoride phosphate (pipzH₂)[MnF₂(HPO₄)(H₂O)](H₂PO₄) can be crystallized. Its structure is built by piperazinium(2+) cations, (H₂PO₄)^? anions, and an anionic double‐chain of [HPO₄] tetrahedra and [MnO₃F₂(H₂O)] octahedra. The structure is triclinic, space group P , Z = 2, a = 622.97(4), b = 923.46(6), c = 1183.62(7) pm, α = 98.343(6)°, β = 100.747(7)°, γ = 107.642(5)°, R = 0.0289. It is worth noting that a ferrodistortive Jahn‐Teller order is observed with [MnO₃F₂(H₂O)] octahedra strongly elongated along the F–Mn–OH₂ axes perpendicular to the chain plane. The structure is stabilized by very strong hydrogen bonds.     

DFT calculations of the defect structures,electronic structures,and EPR parameters for three Rh2+ centers in AgCl

The local structures for various Rh²⁺ centers in AgCl are theoretically studied using density functional theory (DFT) with periodic CP2K program. Through geometry optimizing, the stable ground states with minimal energies and electronic structures are obtained for the tetragonally elongated (T_E), orthorhombically elongated (O_E), and tetragonally compressed (T_C) centers, and the corresponding g and hyperfine coupling tensors are calculated in ORCA level. The calculations reveal obvious Jahn–Teller elongation distortions of about 0.109 and 0.110 Å along [001] axis for T_E and O_E centers without and with 1 next nearest neighbor (nnn) cation vacancy V_Ag in [100] axis, respectively. Whereas T_C center with 1 nnn V_Ag along [001] axis exhibits moderate axial compression of about 0.066 Å due to the Jahn–Teller effect. For O_E and T_C centers with 1 nnn V_Ag, the ligand intervening in the central Rh²⁺ and the V_Ag is found to displace away from the V_Ag by about 0.028 and 0.024 Å, respectively. The present results are discussed and compared with those of the previous calculations based on the perturbation formulas by using the improved ligand field theory.     

S5 graphs as model systems for icosahedral Jahn–Teller problems

The degeneracy of the eigenvalues of the adjacency matrix of graphs may be broken by non-uniform changes of the edge weights. This symmetry breaking is the graph-theoretical equivalent of the molecular Jahn–Teller effect (Ceulemans et al. in Proc Roy Soc 468:971–989, 2012). It is investigated for three representative graphs, which all have the symmetric group on 5 elements, S ₅ , as automorphism group: the complete graph K₅, with 5 nodes, the Petersen graph, with 10 nodes, and an extended K₅ graph with 20 nodes. The spectra of these graphs contain fourfold, fivefold, and sixfold degenerate manifolds, respectively, and provide model systems for the study of the Jahn–Teller effect in icosahedral molecules. The S ₅ symmetries of the distortion modes of the quintuplet in the Petersen graph yield a resolution of the product multiplicity in the corresponding $ H \otimes \left( {g + 2h} \right) $ icosahedral Jahn–Teller problem. In the extended Petersen graph with 20 nodes, a selection rule prevents the Jahn–Teller splitting of the sextuplet into two conjugate icosahedral triplets.