Broken-symmetry DFT Calculations Research Articles

Static and dynamic magnetic properties of the ferromagnetic coordination polymer [Co(NCS)2(py)2]n.

[Co(NCS)2(py)2]n (py = pyridine) is composed of ferromagnetic chains of Co(ii) cations connected by double NCS bridges. The chains are irregular because of two crystallographically inequivalent Co(ii) cations. The coordination polyhedron of the Co(ii) cations is a distorted octahedron built from two N and two S atoms of four equatorial NCS anions and two apical N atoms of the pyridine ligands. Magnetic and specific heat studies show that the compound undergoes a phase transition at 3.7 K to a ferromagnetic state. The determined magnetic interactions, intrachain (J/kB = 28 K) and interchain (zJ'/kB = 0.5 K), confirm the quasi 1D Ising magnetic character of [Co(NCS)2(py)2]n. Using AC magnetic susceptibility measurements the energy barriers for magnetization reversal of different relaxation processes were determined including those of the individual chains. By means of high field-high frequency ESR study the magnetic excitations were observed and explained in the frame of the Ising model in agreement with the results of the magnetic study. Ab initio calculations confirm the high magnetic anisotropy of the system and allow determination of the direction of the easy-axis. The broken symmetry DFT calculations support the ferromagnetic intrachain interactions. The energetic relations relevant for relaxations are discussed. It is concluded that the magnetic model of [Co(NCS)2(py)2]n is not a pure Ising but the transversal exchange plays a role.

Strong intermolecular antiferromagnetic verdazyl-verdazyl coupling in the solid state.

Strong magnetic couplings are generally observed intramolecularly in organic diradicals or in systems in which they are promoted by crystal engineering strategies involving, for example, transition metal ligation. We herein present a strong intermolecularly coupling verdazyl radical in the solid state without the use of such design strategies. The crystal structure of an acetylene-substituted verdazyl radical shows a unique antiparallel face-to-face orientation of the neighboring verdazyl molecules along with verdazyl-acetylene interactions giving rise to an alternating antiferromagnetic Heisenberg chain. Single crystal structural data at 80, 100, 173, and 223 K show that one of the π-stacking distances depends on temperature, while heat capacity data indicate the absence of a phase transition. Based on this structural input, broken symmetry DFT calculations predict a change from an alternating linear Heisenberg chain with two comparable coupling constants J1 and J2 at higher temperatures towards dominant pair interactions at lower temperatures. The predicted antiferromagnetic coupling is confirmed experimentally by magnetic susceptibility, solid-state EPR and NMR spectroscopic results.

Correlated-Participating-Orbitals Pair-Density Functional Method and Application to Multiplet Energy Splittings of Main-Group Divalent Radicals.

Predicting the singlet-triplet splittings of divalent radicals is a challenging task for electronic structure theory. In the present work, we investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) for computing the singlet-triplet splitting for small main-group divalent radicals for which accurate experimental data are available. In order to define theoretical model chemistries that can be assessed consistently, we define three correlated participating orbitals (CPO) schemes (nominal, moderate, and extended, abbreviated as nom, mod, and ext) to define the constitution of complete active spaces, and we test them systematically. Broken-symmetry Kohn-Sham DFT calculations have also been carried out for comparison. We found that the extended CPO-PDFT scheme with translated on-top pair-density functionals have smaller mean unsigned errors than weighted-average broken-symmetry Kohn-Sham DFT with the corresponding exchange-correlation functional. The accuracy of the translated Perdew-Burke-Ernzerhof (tPBE) on-top pair-density functionals with ext-CPO active space is even better than some of the more accurately parametrized exchange-correlation density functionals that we tested; this is very encouraging for MC-PDFT theory.

Redox Switches for Single‐Molecule Magnet Activity: An Ab Initio Insight

A dinuclear Co(II) complex (1) featuring unprecedented anodic and cathodic switches for single-molecule magnet (SMM) activity has been recently investigated (J. Am. Chem. Soc. 2013, 135, 14670). The presence of sandwiched radicals in different oxidation states of this compound mediates magnetic coupling between the high-spin (S=3/2) cobalt ions, which gives rise to SMM activity in both the oxidized ([1(OEt2)](+)) and reduced ([1](-)) states. This feature represents the first example of a SMM exhibiting fully reversible, dual ON/OFF switchability. Here we apply ab initio and broken-symmetry DFT calculations to elucidate the mechanisms responsible for magnetic properties and magnetization blocking in these compounds. It is found that due to the strong delocalization of the magnetic molecular orbital, there is a strong antiferromagnetic interaction between the radical and cobalt ions. The lack of high axiality of the cobalt centres explains why these compounds possess slow relaxation of magnetization only in an applied dc magnetic field.

A tetranuclear nickel(II) heterocubane complex of a bidentate N,O-hydroxymethyl-oxazoline ligand. Synthesis, characterization, magnetic measurements and DFT investigations

Synthesis, structural, and magnetochemical characterization of the tetranuclear [Ni4O4] heterocubane cluster [NiCl(L1)(MeOH)]4, 1, employing the bidentate N,O-ligand 2-hydroxymethyl-2-oxazoline, HL1, is reported. In the solid state, each nickel(II) is coordinated in a distorted octahedral environment, located on four corners of a [Ni4(μ3-O)4] cubane core motif. Measurements of the magnetic susceptibility in solution (Evans method) as well as in the solid state (magnetic susceptibility balance) gave values of 5.74 and 6.08 unpaired electrons, respectively, indicating a spin ground state of S = 3. At maximum spin degeneracy (S = 4), eight unpaired electrons would be expected. Magnetic properties were further evaluated by SQUID measurements of 1, confirming the spin ground state of 1 to be S = 3. The observed deviation is caused by antiferromagnetic coupling between the four Ni atoms. In addition, broken-symmetry DFT calculations confirmed an overlap of magnetic orbitals resulting in exchange coupling between the four nickel(II) ions of 1.

Structural snapshots in the copper(ii) induced azide-nitrile cycloaddition: effects of peripheral ligand substituents on the formation of unsupported μ1,1-azido vs.μ1,4-tetrazolato bridged complexes.

The azido ligand is widely used in coordination chemistry both as a ligand and as a metal-bound reactant. Its role as a bridge for magnetic exchange coupling has attracted a lot of attention in polynuclear metal complexes. However, only a very limited number of complexes are known in which a single azide anion, particularly in the μ1,1-mode, is the only unsupported connection between two metal centers. We present here a series of copper(ii)-azido complexes with amine anchored, triazole-based tripodal ligands containing varying substituents. In the mononuclear copper-azido complexes there is only a negligible effect of these substituents on the structure of the metal complexes. However, the substituents seem to play a decisive role in the type and formation of the dinuclear complexes. Using the tripodal ligand TBTA with flexible benzyl substituents resulted in a rare example of an unsupported and solely μ1,1-azido-bridged dinuclear complex. The use of the TDTA ligand with 2,6-diisopropylphenyl moieties as rigid and sterically demanding substituents resulted in the formation of a scarce example of a solely μ1,4-tetrazolato-bridged dinuclear complex by in situ cycloaddition between the azide and solvent nitrile. This observation of a reaction of unactivated aliphatic nitrile with the azide anion at room temperature is very unusual. The isolation and characterization (by means of X-ray diffraction) of intermediates allows for mechanistic insights into the cycloaddition reaction. The isolated bridges in both dinuclear complexes render them ideal model compounds for the investigation of the magnetic exchange mediated by these ligands usually employed in polynuclear complexes and frameworks together with additional bridging ligands. Magnetic measurements and broken-symmetry DFT calculations were used to shed light on the magnetic exchange revealing weak and moderate antiferromagnetic exchange for the azide and tetrazolate, respectively.

The Mössbauer Parameters of the Proximal Cluster of Membrane-Bound Hydrogenase Revisited: A Density Functional Theory Study.

An unprecedented [4Fe-3S] cluster proximal to the regular [NiFe] active site has recently been found to be responsible for the ability of membrane-bound hydrogenases (MBHs) to oxidize dihydrogen in the presence of ambient levels of oxygen. Starting from proximal cluster models of a recent DFT study on the redox-dependent structural transformation of the [4Fe-3S] cluster, 57Fe Mössbauer parameters (electric field gradients, isomer shifts, and nuclear hyperfine couplings) were calculated using DFT. Our results revise the previously reported correspondence of Mössbauer signals and iron centers in the [4Fe-3S]3+ reduced-state proximal cluster. Similar conflicting assignments are also resolved for the [4Fe-3S]5+ superoxidized state with particular regard to spin-coupling in the broken-symmetry DFT calculations. Calculated 57Fe hyperfine coupling (HFC) tensors expose discrepancies in the experimental set of HFC tensors and substantiate the need for additional experimental work on the magnetic properties of the MBH proximal cluster in its reduced and superoxidized redox states.

Switching nuclearity and Co(II) content through stoichiometry adjustment: {Co(II)6Co(III)3} and {Co(II)Co4(III)} mixed valent complexes and a study of their magnetic properties.

We are reporting two new mixed valent Co(ii)/Co(iii) polynuclear complexes, {Co(II)6Co(III)3} and {Co(II)Co(III)4}, bearing different amount of Co(ii) ions in their cores, through the employment of the multidentate triethanolamine (teaH3) ligand in different stoichiometric ratios. We present a complete picture of the magnetic behaviour of both complexes through a combined usage of the susceptibility, magnetization and X-band EPR data as well as broken-symmetry DFT calculations. Compound shows an atypical spin-only behaviour, probably due to the presence of four and five coordinated Co(ii) sites as well as highly distorted six coordinated Co(ii) ions, promoting a high degree of orbital contribution quenching. Through the usage of a simplified exchange coupling scheme and relying on DFT based magneto-structural correlation we have been able to explain the observed diamagnetic ground state. Concerning compound , DC magnetic data supported by X-band EPR measurements suggest the existence of anisotropy with a zero-field splitting parameter D, at least in the range of 2-10 cm(-1). In agreement with this description, a slow relaxation of magnetization is observed after applying a small external magnetic field, under AC measurements. Field and temperature dependence of the characteristic relaxation time establishes a thermal barrier for magnetization reversal of about 25 cm(-1), which is in good agreement with the energy splitting of the |±1/2〉 and |±3/2〉 doublets established from static magnetic measurements.

Cryptic noninnocence: FeNO corroles in a new light.

Multiple lines of evidence, including electronic absorption spectroscopy, infrared spectroscopy, and broken-symmetry DFT calculations, indicate that the well-known FeNO corroles, long assumed to be {FeNO}(6) complexes, are in fact better described as {FeNO}(7)-(corrole˙(2-)).

Highly Twisted 1,2:8,9-Dibenzozethrenes: Synthesis, Ground State, and Physical Properties

Two soluble and stable 1,2:8,9-dibenzozethrene derivatives (3 a,b) are synthesized through a palladium-catalyzed cyclodimerization reaction. X-ray crystallographic analysis shows that these molecules are highly twisted owing to congestion at the cove region. Broken-symmetry DFT calculations predict that they have a singlet biradical ground state with a smaller biradical character and a large singlet–triplet energy gap; these predictions are supported by NMR and electronic absorption measurements. They have small energy gaps and exhibit far-red/near-infrared absorption/emission and amphoteric redox behaviors.

Modulation of magnetic properties at room temperature: coordination-induced valence tautomerism in a cobalt dioxolene complex.

The valence-tautomeric six-coordinate complex [Co(tbdiox)2(4-papy)2] (1; tbdiox = redox-active 3,5-di-tert-butyl-o-dioxolene, 4-papy = 4-phenylazopyridine) was synthesized and its electronic structure examined. Whereas 1 shows regular thermally driven valence tautomerism in the solid state, it partially dissociates in solution to form the five-coordinate species [Co(tbdiox)2(4-papy)] (2) and free 4-papy. Species 1 and 2 exhibit different electronic structures-low-spin (ls) Co(III) and high-spin (hs) Co(II), respectively-in solution at room temperature and therefore different magnetic properties. Since 1 and 2 are in an equilibrium that is 4-papy-dependent, the magnetic moment of the solution species can be tuned by means of the ligand content. Thus, the concept of coordination-induced valence tautomerism (CIVT) has been introduced. The electronic structures of 1 and 2 as well as their CIVT were elucidated by X-ray crystallography, electrochemistry, titration experiments, and all variable-temperature SQUID susceptometry, NMR, EPR, and electronic absorption spectroscopy. The experimental findings are strongly supported by broken-symmetry DFT calculations. The magnetic exchange interactions in different types of valence-tautomeric cobalt complexes were explored computationally.

1,2,4]Triazolo[4,3-a]pyridines as bridging ligands--magnetism of azole-bridged dinuclear copper(II) complexes influenced by the trigonal distortion parameter τ.

The dinuclear doubly azole-bridged copper(II) complexes [Cu(II)2(L)2(MeCN)4](ClO4)4·3.73MeCN·0.80H2O and [Cu(II)2(L)6](ClO4)4·solvent (solvent = 2MeCN·H2O; 2MeCN·2H2O; 1.5MeOH·3.5H2O) were prepared [L = 3-(6-methyl-2-pyridyl)-[1,2,4]triazolo[4,3-a]pyridine]. Structural characterizations revealed very different local geometries about the copper(II) ions, being trigonal bipyramidal for the former (τ = 0.76) and square pyramidal for the latter (τ = 0.07, 0.15, 0.07) complex. Magnetic measurements of bulk material [Cu(II)2(L)2(H2O)4](ClO4)4 and [Cu(II)2(L)6](ClO4)4·2H2O revealed antiferromagnetic coupling in both complexes, however, of very different strengths. Electron paramagnetic resonance (EPR) spectroscopy was applied to investigate magnetic properties of the complexes in detail. These experimental findings were supported by broken-symmetry DFT calculations. Systematic magneto-structural correlations are discussed.

Broken symmetry DFT calculations of exchange coupling constants for manganese–porphyrin quasi-one-dimensional molecular magnets

We report the results of broken symmetry density functional theory (BS-DFT) calculations providing the exchange coupling constants for two quasi-one-dimensional manganese–porphyrin compounds, [MnOEP][HCBD] and [MnTtBuPP][HCBD] (OEP = octaethylporphyrinato, TtBuPP = meso-tetrakis-(4′-tert-butylphenyl)porphinato, HCBD = hexa-cyanobutadiene). The different magnetic behaviour of these materials is due mainly to the distinct binding modes of the cyanocarbon unit. We compare and contrast the results of BS-DFT calculations for magnetic dinuclears, which properly model the actual molecular magnets, to determine the geometry dependence of the exchange interaction. The exchange coupling constants resulting from BS-DFT calculations vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the constants determined experimentally. Structure-properties correlations reveal the determinant role of the Mn–(N≡C)TCNE bond angle on the ferrimagnetic coupling between the S 1 = 2 spin located on the MnIII–porphyrin donor and the S 2 = 1/2 spin positioned on the cyanocarbon acceptor. Based on a phenomenological model providing the geometry dependence of the exchange coupling constants, we fitted the results of the DFT calculations and obtained parameters describing the ferromagnetic and the antiferromagnetic parts of the superexchange interaction. The large differences between the magnetic properties of the two Mn–HCBD systems are explained based on the correlation between the exchange coupling constant and the overlap between the Mn(III) d and the HCBD π* orbitals and on the torsion angle of the butadiene backbone, which affects dramatically the nature of the π* orbital in the case of the nonplanar HCBD.

Reactivity studies on [Cp′MnX(thf)]2: manganese amide and polyhydride synthesis

The sterically encumbered 1,2,4-(Me3C)3C5H2 (Cp′) ligand allows the synthesis of stable high spin mono(cyclopentadienyl) manganese complexes [Cp′MnX(thf)]2 (X = Cl, Br, I; 1-X). Thermal stabilities of 1-X toward ligand redistribution to [Cp2′Mn] (2) and MnX2 depend on the bridging halide ligand. The kinetic stability of 1-I in solution even at elevated temperatures is noteworthy. Complexes 1 are useful starting materials for further functionalizations. Metathesis of 1-Cl with [LiN(SiMe3)2(OEt2)]2 yields the 13 valence-electron (VE) complex, [Cp′MnN(SiMe3)2] (3), while the manganese polyhydride cluster, [{Cp′Mn}4{MnH6}], was formed in the reaction of 1-I and KHBEt3. The 17 VE [MnH6]4− core of 4 is effectively shielded by four high spin [Cp′Mn]+ units. Magnetic susceptibility studies on 4 suggest weak electron exchange coupling between the spin carriers, but the spin state of the central [MnH6]4− fragment remained ambiguous. Therefore, the electronic structure of 4 was also analyzed by broken symmetry (BS) DFT calculations, which provided strong evidence for a low spin [MnH6]4− unit in agreement with previous spectrochemical studies performed on [FeH6]4−.

High‐Temperature Experimental and Theoretical Study of Magnetic Interactions in Diamond and Pseudo‐Diamond Frameworks Built up from Hexanuclear Tantalum Clusters

Magnetic interactions in solid-state tantalum cluster compounds have been evidenced by using magnetic susceptibility measurements and corroborated by broken-symmetry DFT calculations. The three selected compounds are based on [Ta(6)X(12)(H(2)O)(6)](3+) (X=Cl or/and Br) units with edge-bridged Ta(6) octahedral clusters. Although two of them crystallise in the tetragonal space group I4(1)/a, all compounds exhibit a similar arrangement of paramagnetic clusters related to the diamond structural framework (Fd ̅3m space group). Magnetic parameters were fitted by using the [5,4] Padé approximant of high-temperature series expansion of susceptibility for the Heisenberg model (S=1/2) in the diamond framework, assuming only nearest-neighbouring interactions. Such a model appropriately describes magnetic-susceptibility measurements at temperatures T>0.7|J|/k. The magnetic interaction parameter J between two [Ta(6)Cl(12)(H(2)O)(6)](3+) clusters is estimated to be -64.28(7) cm(-1) ; it has been enhanced by replacing several chlorine inner ligands with bromine ones (J=-123(3) cm(-1) for two [Ta(6)Br(7.7(1))Cl(4.3(1))(H(2)O)(6)](3+) clusters) and is strongest between two bromine [Ta(6)Br(12)(H(2)O)(6)](3+) clusters with a value of -155(1) cm(-1) . Broken-symmetry DFT calculations within spin-dimer analysis confirmed this trend. Those interactions can be explained on the basis of the overlap between singly occupied a(2u) orbitals localised on neighbouring clusters.

Electronic Coupling through Intramolecular π–π Interactions in Biscobaltocenes: A Structural, Spectroscopic, and Magnetic Study

The paramagnetic dinuclear complexes 1,8-bis(cobaltocenyl)naphthalene (2) and 1,8-bis[(pentamethyl-η(5)-cyclopentadienyl)(η(5)-cyclopentadiendiyl)cobalt(II)]naphthalene (4) were synthesized. The molecular structures were characterized by X-ray structure analysis and consisted of two cobaltocenes linked through a distorted naphthalene clamp. Electronic interactions between the two cobalt atoms were observed by cyclic voltammetric studies. Superconducting quantum interference device (SQUID) measurements of the pure compounds and diluted in their diamagnetic iron derivatives, as well as variable-temperature NMR spectroscopy experiments in solution are presented. Magnetic measurements revealed an antiferromagnetic coupling of the electrons in complexes 2 and 4. From NMR spectroscopy experiments, Curie behavior in the temperature range from -60 to +60 °C can be deduced. The electronic structure and magnetic behavior is supported by results of broken-symmetry DFT and multireference calculations along with UV/Vis spectroscopic data, which revealed an intramolecular through space π-π interaction between the cobaltocene units.

The DFT rationalization of exchange and anisotropy in one-dimensional d-p magnets: The [Mn III(porphyrin)][TCNE] case study

We report here numerical experiments, modeling and interpretations dealing with the magnetic interactions necessary for building nano-scale magnets in quasi-one-dimensional systems based on the assembling of [Mn(porphyrin)] + magnetically anisotropic d units and TCNE- p-type spin carriers. The magnetic ordering and its coupling parameter are studied by Broken Symmetry DFT calculations for various model structures, allowing for the rationalization of geometry dependence of the effective exchange. The roles of the phenyl substituent, as well as of the basis set and the DFT functional used in the computation are discussed. The intrinsic anisotropy of these systems is studied in an original manner, extracting Ligand Field and Spin Orbit parameters by combined fits to non-relativistic and relativistic DFT calculations, allowing the explicit estimation of the Zero Field Splitting parameters.

Experimental and theoretical evaluation of magnetic coupling in organometallic radicals: the eloquent case of face-to-face Cp⋯Cp interactions

The solid state magnetic properties of an extensive series of neutral radical (S = ½) complexes associating cyclopentadienyl (Cp) and dithiolene ligands and formulated as [CpNi(dithiolene)]˙, are successfully rationalized through a combination of structural analysis of the crystal structures and broken symmetry DFT calculations. The highly delocalized spin density of these complexes allows for strong antiferromagnetic interactions between radical species, which involve not only short intermolecular S⋯S contacts but also S⋯Cp and Cp⋯Cp contacts, demonstrating that the cyclopentadienyl moiety can effectively act as a non-innocent ligand in metal complexes where it bears a sizeable fraction of the spin density, for example, up to 20% in these [CpNi(dithiolene)]˙ neutral radical complexes.

Ferromagnetic coupled μ-phenoxo-μ-carboxylato heterodinuclear complexes based on the Cr(salen) moiety: structural and magnetic characterization

The synthesis, crystal structure, and magneto-chemical characterization of two new unprecedented -phenoxo--carboxylato heterodinuclear complexes based on the Cr(salen) moiety (salen = N,N-bis(salicylidene)ethylenediamine), [MII(O2C(CH3)3)(OH2)2(mu-O2C(CH3)3)(-salen)CrIII(O2C(CH3)3)], M = Ni (2), Co(3) are reported. The dinuclear complexes were obtained starting from the mononuclear trans-[Cr(salen)(CN)2]PPh4 (1), whose crystal structure is also reported. They show a trans arrangement of the Cr(salen) unit, bridging through the phenolate O atoms to a second metal center. An additional 2-O2-carboxylato bridge and a further monodentating carboxylate ligand complete the roughly octahedral Cr(III) coordination sphere. The highly distorted octahedral M(II) coordination environment is completed by two coordinated water molecules and an additional monodentating carboxylate. Variable-temperature solid-state DC magnetization studies were carried out in the 2.0-300 K range. Ferromagnetic isotropic pairwise exchange parameters were found with values of J = 4.1 cm-1 (2) and J = 2.1 cm-1 (3). Additionally, for complex 3, a ZFS parameter, D, was employed to properly fit the experimental data. Magnetization (M) vs. field (H) and temperature (T) data further support the presence of this anisotropic component and confirm ground states S = 5/2 and S = 3 for 2 and 3, respectively. Broken symmetry DFT calculations properly reproduce the experimental J values supporting the ferromagnetic exchange interaction experimentally observed. No out of phase susceptibility signal was observed in 0 DC magnetic field for both complexes. However, in the case of complex 3 a non-zero is observed when a small external field is applied below 3 K, suggesting slow relaxation of the magnetization which at 0 DC field is suppressed, probably due to efficient tunnelling relaxation pathways. The low symmetry of the Co(II) site in complex 3 may lead to the presence of transversal anisotropic components which could be responsible for the enhanced tunnelling pathway.

“Structural and magnetic characterization of a 1D chain of [Co(II)2(μ-aqua)(μ-carboxylate)2] strung cores”

A novel 1D chain built up from stringing of [Co2(mu-OH2)(mu-O2CC(CH3)3)2] units with the bridging 2,2'-bipyrimidine ligand has been synthesized and structurally characterized. The chains are well isolated from each other by the bulky tert-butyl groups of the carboxlyates and show an alternating zigzag configuration for the Co(II) metallic centres. DC magnetic measurements show anti-ferromagnetic coupling, Jca.-3 cm(-1) between adjacent Co(II) ions along the chain. Noticeably, good data fitting was obtained by means of simple models that neglect any kind of first order orbital contribution to the spin ground state, which is normally observed in Co(II) complexes. These results were further confirmed by broken-symmetry DFT calculations performed on a tetranuclear model emulating the 1D chain structure. Field dependence magnetization measurements show an incipient field-induced energy level crossing at high magnetic field and low temperature (1.8 K).