Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

Construction of Ideal One-Dimensional Spin Chains by Topochemical Dehydration/Rehydration Route

One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet achieved through a multistep topochemical route involving dehydration and rehydration. By desorbing three water molecules from (2,2'-bpy)FeF3(H2O)·2H2O (2,2'-bpy = 2,2'-bipyridyl) at 150 °C and then intercalating two water molecules at room temperature (giving (2,2'-bpy)FeF3·2H2O 1), the initially isolated FeF3ON2 octahedra combine to form corner-sharing FeF4N2 octahedral chains, which are effectively separated by organic and added water molecules. Mössbauer spectroscopy reveals significant dynamical fluctuations down to 2.7 K, despite the presence of strong intrachain interactions. Moreover, results from electron spin resonance (ESR) and heat capacity measurements indicate the absence of long-range order down to 0.5 K. This controlled topochemical dehydration/rehydration approach is further extended to (2,2'-bpy)CrF3·2H2O with S = 3/2 1D chains, thus opening the possibility of obtaining other low-dimensional spin lattices.

Low-Dimensional Metal-Organic Magnets as a Route toward the S = 2 Haldane Phase

Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are connected by organic linkers, are promising candidates for next-generation quantum technologies. MOMs readily form low-dimensional structures and so are ideal systems to realize physical examples of key quantum models, including the Haldane phase, where a topological excitation gap occurs in integer-spin antiferromagnetic (AFM) chains. Thus, far the Haldane phase has only been identified for S = 1, with S ≥ 2 still unrealized because the larger spin imposes more stringent requirements on the magnetic interactions. Here, we report the structure and magnetic properties of CrCl2(pym) (pym = pyrimidine), a new quasi-1D S = 2 AFM MOM. We show, using X-ray and neutron diffraction, bulk property measurements, density-functional theory calculations, and inelastic neutron spectroscopy (INS), that CrCl2(pym) consists of AFM CrCl2 spin chains (J1 = -1.13(4) meV) which are weakly ferromagnetically coupled through bridging pym (J2 = 0.10(2) meV), with easy-axis anisotropy (D = -0.15(3) meV). We find that, although small compared to J1, these additional interactions are sufficient to prevent observation of the Haldane phase in this material. Nevertheless, the proximity to the Haldane phase together with the modularity of MOMs suggests that layered Cr(II) MOMs are a promising family to search for the elusive S = 2 Haldane phase.

From an antiferromagnetic insulator to a strongly correlated metal in square-lattice MCl2(pyrazine)2 coordination solids

Electronic synergy between metal ions and organic linkers is a key to engineering molecule-based materials with a high electrical conductivity and, ultimately, metallicity. To enhance conductivity in metal-organic solids, chemists aim to bring the electrochemical potentials of the constituent metal ions and bridging organic ligands closer in a quest to obtain metal-d and ligand-π admixed frontier bands. Herein, we demonstrate the critical role of the metal ion in tuning the electronic ground state of such materials. While VCl₂(pyrazine)₂ is an electrical insulator, TiCl₂(pyrazine)₂ displays the highest room-temperature electronic conductivity (5.3 S cm^-1) for any metal-organic solid involving octahedrally coordinated metal ions. Notably, TiCl₂(pyrazine)₂ exhibits Pauli paramagnetism consistent with the specific heat, supporting the existence of a Fermi liquid state (i.e., a correlated metal). This result widens perspectives for designing molecule-based systems with strong metal-ligand covalency and electronic correlations.

Magneto-structural Correlations in Ni2+-Halide···Halide-Ni2+ Chains

We present the magnetic properties of a new family of S = 1 molecule-based magnets, NiF₂(3,5-lut)₄·2H₂O and NiX₂(3,5-lut)₄, where X = HF₂, Cl, Br, or I (lut = lutidine C₇H₉N). Upon creation of isolated Ni–X···X–Ni and Ni–F–H–F···F–H–F–Ni chains separated by bulky and nonbridging lutidine ligands, the effect that halogen substitution has on the magnetic properties of transition-metal-ion complexes can be investigated directly and in isolation from competing processes such as Jahn–Teller distortions. We find that substitution of the larger halide ions turns on increasingly strong antiferromagnetic interactions between adjacent Ni²⁺ ions via a novel through-space two-halide exchange. In this process, the X···X bond lengths in the Br and I materials are more than double the van der Waals radius of X yet can still mediate significant magnetic interactions. We also find that a simple model based on elongation/compression of the Ni²⁺ octahedra cannot explain the observed single-ion anisotropy in mixed-ligand compounds. We offer an alternative that takes into account the difference in the electronegativity of axial and equatorial ligands.

The magnetic properties of well-separated Ni²⁺ chains are highly dependent on the bridging halide ligands. By increasing the size of the halide ions, we can decrease the single-ion anisotropy such that the system moves from easy plane to easy axis. Through-space magnetic interactions between adjacent Ni²⁺ ions are also turned on as the larger halides are substituted into the exchange pathway.

Tight-Binding Approach to Pyrazine-Mediated Superexchange in Copper-Pyrazine Antiferromagnets

We investigate the cause of spatial superexchange anisotropy in a family of copper-based, quasi-two-dimensional materials with very similar geometries. The compounds in this family differ mainly in their inter-layer separation but they have very different magnetic interactions, even within the basal plane. We use density functional theory and Wannier functions to parameterize two complimentary tight-binding models and show that the superexchange between the Cu²⁺ ions is dominated by a σ-mediated interaction between hybrid Cu-pyrazine orbitals centered on the copper atoms. We find no correlations between the strength of this exchange interaction and homologous geometric features across the compounds, such as Cu and pyrazine bond lengths and orientations of nearby counterions. We find that the pyrazine tilt angles do not affect the Cu-pyrazine-Cu exchange because the lowest unoccupied molecular orbital on pyrazine is at a very high energy (relative to the frontier orbitals, which are Cu-based). We conclude that careful control of the entire crystal structure, including non-homologous geometric features such as the inter-layer organic ligands, is vital for engineering magnetic properties.

Pyrazine-bridged Cu(ii) chains: diaquabis(n-methyl-2-pyridone)copper(ii) perchlorate complexes

A family of pyrazine-bridged, linear chain complexes of Cu(ii) of the formula [CuL₂(H₂O)₂(pz)](ClO₄)₂ [pz = pyrazine; L = n-methyl-2(1H)-pyridone, n = 3 (1), 5 (2), and 6 (3)] has been prepared. Single-crystal X-ray diffraction shows six-coordinate, pyrazine-bridged chains with trans-pairs of ancillary ligands. The substituted pyridine molecules exist in their pyridone tautomers and are coordinated through the carbonyl oxygen atom. The structure is stabilized by intramolecular hydrogen bonds between the pyridone and water molecule, and via hydrogen bonds between the water molecules and perchlorate ions. 2 undergoes a crystallographic phase transition between C2/c (high temperature phase) and P1[combining macron] (low temperature phase). Powder EPR spectra reveal that all complexes are rhombic, although differences between g_x and g_y can only be seen clearly at Q-band. Variable temperature magnetic susceptibility data show antiferromagnetic interactions and the data were fit to the uniform chain model yielding J/k_B = -9.8, -9.2 and -11 K for 1-3 respectively. Attempts to model an interchain interaction strength indicate that the chains are very well isolated.

Spin Density Topology

Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin density critical points, the 18 different ways in which they can be realized and the peculiar topological constraints on their number and kind, arising from the presence of positive and negative spin density regions, is addressed. The notion of molecular spin graphs, spin maxima (minima) joining paths, spin basins and of their valence is introduced. We show that two kinds of structures are associated with a spin-polarized molecule: the usual one, defined through the electron density gradient, and the magnetic structure, defined through the spin density gradient and composed in general by at least two independent spin graphs, related to spin density maxima and minima. Several descriptors, such as the spin polarization index, are introduced to characterize the properties of spin density critical points and basins. The study on the general features of the spin density topology is followed by the specific example of the water molecule in the ³B₁ triplet state, using spin density distributions of increasing accuracy.

Magnetic Network on Demand: Pressure Tunes Square Lattice Coordination Polymers Based on {[Cu(pyrazine)2]2+}n

We report the pressure-induced structural and magnetic changes in [CuCl(pyz)₂](BF₄) (pyz = pyrazine) and [CuBr(pyz)₂](BF₄), two members of a family of three-dimensional coordination polymers based on square mesh {[Cu(pyz)₂]²⁺}_n layers. High-pressure X-ray diffraction and density functional theory calculations have been used to investigate the structure-magnetic property relationship. Although structurally robust and almost undeformed within a large pressure range, the {[Cu(pyz)₂]²⁺}_n network can be electronically modified by adjusting the interaction of the apical linkers interconnecting the layers, which has strong implications for the magnetic properties. It is then demonstrated that the degree of covalent character of the apical interaction explains the difference in magnetic exchange between the two species. We have also investigated the mechanical deformation of the network induced by nonhydrostatic compression that affects the structure depending on the crystal orientation. The obtained results suggest the existence of "Jahn-Teller frustration" triggered at the highest hydrostatic pressure limit.

Electron Density and Dielectric Properties of Highly Porous MOFs: Binding and Mobility of Guest Molecules in Cu3(BTC)2 and Zn3(BTC)2

Two isostructural highly porous metal-organic frameworks, the well-known {Cu₃(BTC)₂} _n (BTC = 1,3,5-benzenetricarboxylate), often appointed with the name HKUST-1, and {Zn₃(BTC)₂} _n, have been investigated as models for the buildup of dielectric properties, differentiating the role of chemi- and physisorbed guest molecules and that of specific intraframework and framework-guest linkages. For this purpose, electron charge density analysis, impedance spectroscopy, density functional theory simulations, and atomic partitioning of the polarizabilities have been exploited. These analyses at different degrees of pores filling enabled one to observe structural and electronic changes induced by guest molecules, especially when chemisorbed. The electrostatic potential inside the pores allows one to describe the absorption mechanism and to estimate the polarization of guests induced by the framework. The dielectric constant shows very diverse frequency dependence and magnitude of real and imaginary components as a consequence of (I) capture of guest molecules in the pores during synthesis, (II) MOF activation, and (III) water absorption from the atmosphere after activation. Comparison with calculated static-dielectric constant and atomic polarizabilities of the material has allowed for evaluating building blocks' contribution to the overall property, paving the way for reverse crystal engineering of these species.

Magnetic order and enhanced exchange in the quasi-one-dimensional molecule-based antiferromagnet Cu(NO3)2(pyz)3

The quasi-one-dimensional molecule-based Heisenberg antiferromagnet Cu(NO₃)₂(pyz)₃ has an intrachain coupling J = 13.7(1) K () and exhibits a state of long-range magnetic order below T_N = 0.105(1) K. The ratio of interchain to intrachain coupling is estimated to be |J'/J| = 3.3 × 10^-3, demonstrating a high degree of isolation for the Cu chains.

Giant Pressure Dependence and Dimensionality Switching in a Metal-Organic Quantum Antiferromagnet

We report an extraordinary pressure dependence of the magnetic interactions in the metal-organic system [CuF_{2}(H_{2}O)_{2}]_{2}pyrazine. At zero pressure, this material realizes a quasi-two-dimensional spin-1/2 square-lattice Heisenberg antiferromagnet. By high-pressure, high-field susceptibility measurements we show that the dominant exchange parameter is reduced continuously by a factor of 2 on compression. Above 18 kbar, a phase transition occurs, inducing an orbital re-ordering that switches the dimensionality, transforming the quasi-two-dimensional lattice into weakly coupled chains. We explain the microscopic mechanisms for both phenomena by combining detailed x-ray and neutron diffraction studies with quantitative modeling using spin-polarized density functional theory.

Charge density study of bis(clonixato)bis(ethanol) bis(imidazole)copper(II) complex

An experimental electronic structure of bis(clonixato)bis(ethanol) bis(imidazole)copper(II) complex, [Cu(cln)2(im)2(EtOH)2] (cln=clonixato, im=imidazole) (1) has been obtained from single-crystal X-ray diffraction data collected at 100 K using an Incoatec IμS Ag microfocus source. Metal-ligand (ML) bonds and hydrogen bonds (HBs) have been analysed using topological analysis of the experimental electron density with the atoms in molecules (AIM) approach. The central copper atom is octahedrally coordinated by two oxygen atoms from two clonixato anions and two nitrogen atoms from two imidazole ligands in equatorial plane. In axial positions are two oxygen atoms from two ethanol molecules. AIM analysis establishes that the central copper atom is bonded more strongly to the clonixato anion that to the imidazole or ethanol molecules. AIM analysis of two intramolecular and one intermolecular hydrogen bonds permits to estimate their strength. We show that the hydrogen bonds are strong enough to protect the molecule from decomposition in solvent media and to disable the more reactive imidazole-Cu-clonixato complex from interacting with e.g. a macromolecule. The electrostatic potential of the complex shows a highly positive value on the central atom, so the complex is highly reactive in an interaction with negative ligands.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl and Br

Two Cu²⁺ coordination polymers [CuCl(pyz)₂](BF₄) 1 and [CuBr(pyz)₂](BF₄) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)₂]²⁺ magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single-crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)₂]²⁺ layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at ∼8 K, indicating antiferromagnetic interactions within the [Cu(pyz)₂]²⁺ layers. 2D Heisenberg model fits result in J_∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with | J_⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below T_N = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis ( k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) μ_B/Cu²⁺ for 1 and 0.6(1) μ_B/Cu²⁺ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu²⁺ g-tensor was determined from electron spin resonance spectra as g _x = 2.060(1), g _z = 2.275(1) for 1 and g _x = 2.057(1), g _z = 2.272(1) for 2 at room temperature.

Insights on spin delocalization and spin polarization mechanisms in crystals of azido copper(II) dinuclear complexes through the electron spin density Source Function

The Source Function (SF) tool was applied to the analysis of thetheoreticalspin density in azido CuIIdinuclear complexes, where the azido group, acting as a coupler between the CuIIcations, is linked to the metal centres either in an end-on or in an end–end fashion. Results for only the former structural arrangement are reported in the present paper. The SF highlights to which extent the magnetic centres contribute to determine the local spin delocalization and polarization at any point in the dimetallic complex and whether an atom or group of atoms of the ligands act in favour or against a given local spin delocalization/polarization. Ball-and-stick atomic SF percentage representations allow for a visualization of the magnetic pathways and of the specific role played by each atom along these paths, at given reference points. Decomposition of SF contributions in terms of a magnetic and of a relaxation component provides further insight. Reconstruction of partial spin densities by means of the Source Function has for the first time been introduced. At variance with the standard SF percentage representations, such reconstructions offer a simultaneous view of the sources originating from specific subsets of contributing atoms, in a selected molecular plane or in the whole space, and are therefore particularly informative. The SF tool is also used to evaluate the accuracy of the analysed spin densities. It is found that those obtained at the unrestricted B3LYP DFT level, relative to those computed at the CASSCF(6,6) level, greatly overestimate spin delocalization to the ligands, but comparatively underestimate magnetic connection (spin transmission) among atoms, along the magnetic pathways. As a consequence of its excessive spin delocalization, the UB3LYP method also overestimates spin polarization mechanisms between the paramagnetic centres and the ligands. Spin delocalization measures derived from the refinement of Polarized Neutron Diffraction data seem in general superior to those obtained through the DFT UB3LYP approach and closer to the far more accurate CASSCF results. It is also shown that a visual agreement on the spin-resolved electron densities ραand ρβderived from different approaches does not warrant a corresponding agreement between their associated spin densities.

Validation of experimental charge-density refinement strategies: when do we overfit?

A cross-validation method is supplied to judge between various strategies in multipole refinement procedures. Its application enables straightforward detection of whether the refinement of additional parameters leads to an improvement in the model or an overfitting of the given data. For all tested data sets it was possible to prove that the multipole parameters of atoms in comparable chemical environments should be constrained to be identical. In an automated approach, this method additionally delivers parameter distributions of k different refinements. These distributions can be used for further error diagnostics, e.g. to detect erroneously defined parameters or incorrectly determined reflections. Visualization tools show the variation in the parameters. These different refinements also provide rough estimates for the standard deviation of topological parameters.

Sustainable Synthesis of Balsalazide and Sulfasalazine Based on Diazotization with Low Concentrations of Nitrogen Dioxide in Air

Low concentrations of nitrogen dioxide, which arises as a side product from a range of industrial processes, can effectively be recycled through the diazotization of anilines. The studies reported herein now demonstrate that the removal of nitrogen dioxide from gas streams is even more effective when hydrophilic anilines are used as starting materials. The diazonium salts, which are obtained in this way in up to quantitative yields, can directly be employed in azo coupling reactions, thus opening up an attractive route to the industrially important group of azo compounds.

Bimetallic MOFs (H3O)x[Cu(MF6)(pyrazine)2]·(4 − x)H2O (M = V4+, x = 0; M = Ga3+, x = 1): co-existence of ordered and disordered quantum spins in the V4+ system

These bimetallic MOFs contain [Cu(pyz)₂]²⁺ sheets and MF₆ⁿ⁻ octahedra whereby only the Cu(ii) moments magnetically order.