Electron-spin magnetic moments of the 2Σ+ ions Li2+, Li2−, and Be2+: An ab initio ROHF study

For the ²Σ⁺ ground states of the ions Li₂⁺, Li₂⁻, and Be₂⁺, the dependence of the magnetic moment (parametrized by g-shifts) on the bond length R was studied at the ROHF level. The Δ g-values were calculated via a perturbative approach (complete to second order in Breit-Pauli interactions) using quadruple-zeta AO basis sets augmented by semidiffuse and polarization functions. All Δ g-values in these systems are negative. The parallel component Δ g_∥ generally changes little with R, remaining close to the g-shift of the corresponding ²S atomic dissociation product. For Li₂⁺ and Be₂⁺, the perpendicular component Δ g _⟂ is more sensitive to geometry than is Δ g_∥, mainly because of the second-order magnetic coupling with excited ²Π states. For Li₂⁻, Δ g _⟂ and Δ g_∥ are similar due to the large size of the 2σ_u, SOMO, resulting in g-values close to that of a free electron. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 511–521, 1997     

Study of the Light‐Induced Spin Crossover Process of the [FeII(bpy)3]2+ Complex

Ab initio calculations have been performed on [Fe^II(bpy)₃]²⁺ (bpy=bipyridine) to establish the variation of the energy of the electronic states relevant to light‐induced excited‐state spin trapping as a function of the Fe? ligand distance. Light‐induced spin crossover takes place after excitation into the singlet metal‐to‐ligand charge‐transfer (MLCT) band. We found that the corresponding electronic states have their energy minimum in the same region as the low‐spin (LS) state and that the energy dependence of the triplet MLCT states are nearly identical to the ¹MLCT states. The high‐spin (HS) state is found to cross the MLCT band near the equilibrium geometry of the MLCT states. These findings give additional support to the hypothesis of a fast singlet–triplet interconversion in the MLCT manifold, followed by a ³MLCT–HS (⁵T₂) conversion accompanied by an elongation of the Fe? N distance.     

Electronic structure,magnetic properties,and mixed valence character of Ce2Ni3Si5 from first principles calculations

Cerium intermetallic compounds exhibit anomalous physical properties such as heavy fermion and Kondo behaviors. Here, an ab initio study of the electronic structure, magnetic properties, and mixed valence character of Ce₂Ni₃Si₅ using density functional theory (DFT) is presented. Two theoretical methods, including pure Perdew–Burke–Ernzerhof (PBE) and PBE + U , are used. In this study, Ce³⁺ and Ce⁴⁺ are considered as two different constituents in the unit cell. The formation energy calculations on the DFT level propose that Ce is in a stable mixed valence of 3.379 at 0 K. The calculated electronic structure shows that Ce₂Ni₃Si₅ is a metallic compound with a contribution at the Fermi level from Ce 4f and Ni 3d states. With the inclusion of the effective Hubbard parameter (U _eff), the five valence electrons of 5 Ce³⁺ ions are distributed only on Ce³⁺ 4f orbitals. Therefore, the occupied Ce³⁺ 4f band is located in the valence band (VB) while Ce⁴⁺ 4f orbitals are empty and Located at the Fermi level. The calculated magnetic moment in Ce₂Ni₃Si₅ is only due to cerium (Ce³⁺) in good agreement with the experimental results. The U _eff value of 5.4 eV provides a reasonable magnetic moment of 0.981 for the unpaired electron per Ce³⁺ ion. These results may serve as a guide for studying present mixed valence cerium‐based compounds. © 2017 Wiley Periodicals, Inc.     

Remarkable Energy Barrier for Magnetization Reversal in 3D and 2D Dysprosium-Chloranilate-Based Coordination Polymers

Herein, two coordination polymers (CPs) [{Dy(Cl₂An)_1.5(CH₃OH)} ⋅ 4.5 H₂O]_n ( 1 ) and [Dy(Cl₂An)_1.5(DMF)₂]_n ( 2 ), in which Cl₂An is chloranilate (2,5-dihydroxy-1,4-benzoquinone dianion), exhibiting field-induced single-molecule magnet behavior with moderate barrier of magnetization reversal are reported. Detailed structural and topological analysis disclosed that 1 has a 3D network, whereas 2 has a 2D layered-type structure. In both CPs, magnetic measurements showed weak antiferromagnetic exchange interaction between the dysprosium centers and field-induced slow magnetic relaxation with barriers of 175(9)K and 145(7)K for 1 and 2 , respectively. Notably, the energy barriers of magnetization reversal of 1 and 2 are remarkable for metal–chloranilate-based 3D ( 1 ) and 2D ( 2 ) CPs. The temperature and field dependence of relaxation time indicate the presence of multiple relaxation pathways, such as direct, quantum tunneling of magnetization, Raman, and Orbach processes, in both CPs. Ab initio theoretical calculations reinforced the experimentally observed higher energy barrier in 1 as compared with 2 due to the presence of large transverse anisotropy in the ground state in the latter. The average transition magnetic moment between the computed low-lying spin–orbit states also rationalized the relaxation as Orbach and Raman processes through the first excited state. BS-DFT calculations were carried out for both CPs to provide more insight into the exchange interaction.     

Magnetic Coupling Constants of Self‐Assembled CuII [3×3] Grids: Alternative Spin Model from Theoretical Calculations

This paper reports a theoretical analysis of the electronic structure and magnetic properties of a ferromagnetic Cu^II [3×3] grid. A two‐step strategy, combining calculations on the whole grid and on binuclear fragments, has been employed to evaluate all the magnetic interactions in the grid. The calculations confirm an S=7/2 ground state, which is in accordance with the magnetisation versus field curve and the thermal dependence of the magnetic moment data. Only the first‐neighbour coupling terms present non‐negligible amplitudes, all of them in agreement with the structure and arrangement of the Cu 3d magnetic orbitals. The results indicate that the dominant interaction in the system is the antiferromagnetic coupling between the ring and the central Cu sites (J₃=J₄≈?31 cm^?1). In the ring two different interactions can be distinguished, J₁=4.6 cm^?1 and J₂=?0.1 cm^?1, in contrast to the single J model employed in the magnetic data fit. The calculated J values have been used to determine the energy level distribution of the Heisenberg magnetic states. The effective magnetic moment versus temperature plot resulting from this ab initio energy profile is in good agreement with the experimental curve and the fitting obtained with the simplified spin model, despite the differences between these two spin models. This study underlines the role that the theoretical evaluations of the coupling constants can play on the rationalisation of the magnetic properties of these complex polynuclear systems.     

Application of the Perimeter Model to the Assignment of the Electronic Absorption Spectra of Gold(III) Hexaphyrins with [4n+2] and [4n] π‐Electron Systems

Expanded porphyrins : The electronic excited states of two forms of meso‐hexakis(pentafluorophenyl)‐substituted gold(III) hexaphyrin(1.1.1.1.1.1), such as that depicted, have been investigated by density functional calculations and magnetic circular dichroism spectroscopy to assign their low‐energy excited singlet states.

     

Two C3‐Symmetric Dy3III Complexes with Triple Di‐μ‐methoxo‐μ‐phenoxo Bridges,Magnetic Ground State,and Single‐Molecule Magnetic Behavior

Two series of isostructural C₃‐symmetric Ln₃ complexes Ln₃ ? [BPh₄] and Ln₃ ? 0.33[Ln(NO₃)₆] (in which Ln^III=Gd and Dy) have been prepared from an amino‐bis(phenol) ligand. X‐ray studies reveal that Ln^III ions are connected by one μ₂‐phenoxo and two μ₃‐methoxo bridges, thus leading to a hexagonal bipyramidal Ln₃O₅ bridging core in which Ln^III ions exhibit a biaugmented trigonal‐prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self‐consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy^III ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy?O distance, the local magnetic moments are oriented almost perpendicular to the Dy₃ plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy^III ions are separated by approximately 150 and 177 cm^?1, for Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆], respectively. As expected for these large energy gaps, Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆] exhibit, under zero direct‐current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied H_dc field of 1000 Oe, Dy₃ ? [BPh₄] exhibits two thermally activated processes with U_eff values of 34.7 and 19.5 cm^?1, whereas Dy₃ ? 0.33[Dy(NO₃)₆] shows only one activated process with U_eff=19.5 cm^?1.     

Unraveling σ and π Effects on Magnetic Anisotropy in cis‐NiA4B2 Complexes: Magnetization,HF‐HFEPR Studies,First‐Principles Calculations,and Orbital Modeling

By using complementary experimental techniques and first‐principles theoretical calculations, magnetic anisotropy in a series of five hexacoordinated nickel(II) complexes possessing a symmetry close to C_2v, has been investigated. Four complexes have the general formula [Ni(bpy)X₂]ⁿ⁺ (bpy=2,2′‐bipyridine; X₂=bpy ( 1 ), (NCS^?)₂ ( 2 ), C₂O₄^2? ( 3 ), NO₃^? ( 4 )). In the fifth complex, [Ni(HIM₂‐py)₂(NO₃)]⁺ ( 5 ; HIM₂‐py=2‐(2‐pyridyl)‐4,4,5,5‐tetramethyl‐4,5‐dihydro‐1H‐imidazolyl‐1‐hydroxy), which was reported previously, the two bpy bidentate ligands were replaced by HIM₂‐py. Analysis of the high‐field, high‐frequency electronic paramagnetic resonance (HF‐HFEPR) spectra and magnetization data leads to the determination of the spin Hamiltonian parameters. The D parameter, corresponding to the axial magnetic anisotropy, was negative (Ising type) for the five compounds and ranged from ?1 to ?10 cm^?1. First‐principles SO‐CASPT2 calculations have been performed to estimate these parameters and rationalize the experimental values. From calculations, the easy axis of magnetization is in two different directions for complexes 2 and 3 , on one hand, and 4 and 5 , on the other hand. A new method is proposed to calculate the g tensor for systems with S=1. The spin Hamiltonian parameters (D (axial), E (rhombic), and g_i) are rationalized in terms of ordering of the 3 d orbitals. According to this orbital model, it can be shown that 1) the large magnetic anisotropy of 4 and 5 arises from splitting of the e_g‐like orbitals and is due to the difference in the σ‐donor strength of NO₃^? and bpy or HIM₂‐py, whereas the difference in anisotropy between the two compounds is due to splitting of the t_2g‐like orbitals; and 2) the anisotropy of complexes 1 – 3 arises from the small splitting of the t_2g‐like orbitals. The direction of the anisotropy axis can be rationalized by the proposed orbital model.     

Banana-shaped molecules peculiarly oriented in a magnetic field: (2)H NMR spectroscopy and quantum mechanical calculations.

The orientational properties of the banana-shaped liquid crystal 4-chloro-1,3-phenylenebis{4-[4'-(10-undecenyloxy)]benzoyloxy} benzoate (ClPbis11BB) are reported in the nematic phase under the effect of an external magnetic field. A new hypothesis, which states that the central ring of the aromatic core is oriented perpendicularly to the external magnetic field, is proposed. In support of this hypothesis, a series of studies based on (2)H NMR spectroscopy, both in the bulk and in solution, are discussed. (2)H NMR measurements on three selectively deuterium-labelled isotopomers are presented, together with DFT results from B3LYP/cc-pvDz calculations performed on the aromatic core. The rather flat shape of the investigated intramolecular energy surface allows for several different conformations to be populated, the computed magnetic susceptibilities of which are consistent with the proposed hypothesis of peculiar orientation of banana-shaped molecules. Moreover, the orientation of the magnetic susceptibility tensor is shown to be strongly dependent on the internal conformation of the banana-shaped molecules.     

Ultrafast Deactivation Mechanism of the Excited Singlet in the Light‐Induced Spin Crossover of [Fe(2,2′‐bipyridine)3]2+

The mechanism of the light‐induced spin crossover of the [Fe(bpy)₃]²⁺ complex (bpy=2,2′‐bipyridine) has been studied by combining accurate electronic‐structure calculations and time‐dependent approaches to calculate intersystem‐crossing rates. We investigate how the initially excited metal‐to‐ligand charge transfer (MLCT) singlet state deactivates to the final metastable high‐spin state. Although ultrafast X‐ray free‐electron spectroscopy has established that the total timescale of this process is on the order of a few tenths of a picosecond, the details of the mechanisms still remain unclear. We determine all the intermediate electronic states along the pathway from low spin to high spin and give estimates for the deactivation times of the different stages. The calculations result in a total deactivation time on the same order of magnitude as the experimentally determined rate and indicate that the complex can reach the final high‐spin state by means of different deactivation channels. The optically populated excited singlet state rapidly decays to a triplet state with an Fe d⁶(${{\rm t}{{5\hfill \atop {\rm 2g}\hfill}}}$ ${{\rm e}{{1\hfill \atop {\rm g}\hfill}}}$ ) configuration either directly or by means of a triplet MLCT state. This triplet ligand‐field state could in principle decay directly to the final quintet state, but a much faster channel is provided by internal conversion to a lower‐lying triplet state and subsequent intersystem crossing to the high‐spin state. The deactivation rate to the low‐spin ground state is much smaller, which is in line with the large quantum yield reported for the process.     

Three‐Axis Anisotropic Exchange Coupling in the Single‐Molecule Magnets NEt4[MnIII2(5‐Brsalen)2(MeOH)2MIII(CN)6] (M=Ru,Os)

We have investigated the single‐molecule magnets [Mn^III₂(5‐Brsalen)₂(MeOH)₂M^III(CN)₆]NEt₄ (M=Os ( 1 ) and Ru ( 2 ); 5‐Brsalen=N,N′‐ethylenebis(5‐bromosalicylidene)iminate) by frequency‐domain Fourier‐transform terahertz electron paramagnetic resonance (THz‐EPR), inelastic neutron scattering, and superconducting quantum interference device (SQUID) magnetometry. The combination of all three techniques allows for the unambiguous experimental determination of the three‐axis anisotropic magnetic exchange coupling between Mn^III and Ru^III or Os^III ions, respectively. Analysis by means of a spin‐Hamiltonian parameterization yields excellent agreement with all experimental data. Furthermore, analytical calculations show that the observed exchange anisotropy is due to the bent geometry encountered in both 1 and 2 , whereas a linear geometry would lead to an Ising‐type exchange coupling.     

Seeking Hidden Magnetic Phenomena by Theoretical Means in a Thiooxoverdazyl Adduct

The oxidation of 1,5‐dimethyl‐3‐(2′‐pyridyl)‐6‐thiooxotetrazane (SvdH₃py) by benzoquinone leads to a 1:1 adduct of 1,5‐dimethyl‐3‐(2′‐pyridyl)‐6‐thiooxoverdazyl radical (Svdpy) with hydroquinone (hq). The single‐crystal X‐ray diffraction of this adduct at room temperature (RT) shows that the radicals exhibit a slight curvature that leads to the formation of alternating head‐to‐tail (antiparallel) stacked 1D chains. Moreover, temperature‐dependent X‐ray measurements at 100, 200, and 303 K reveal that the lateral slippages between the radicals of the stacks |δ₁| and |δ₂| vary from 0.64 to 0.78 Å and 0.54 to 0.40 Å between 100 and 303 K. Despite the alternation of the inter‐radical distances and lateral slippages, the magnetic susceptibility data can be fitted with excellent agreement using a regular one‐dimensional antiferromagnetic chain model with J=?5.9 cm^?1. Wavefunction‐based calculations indicate an alternation of the magnetic interaction parameters correlated with the structural analysis at RT. Moreover, they demonstrate that the thermal slippage of the radicals induces a switching of the physical behavior, since the exchange interaction changes from antiferromagnetic (?0.9 cm^?1) at 100 K to ferromagnetic (1.4 cm^?1) at 303 K. The theoretical approach thus reveals a much richer magnetic behavior than the analysis of the magnetic susceptibility data and ultimately questions the relevance of a spin‐coupled picture based on temperature‐independent parameters.     

Rational Design of a Confacial Pentaoctahedron: Anisotropic Exchange in a Linear ZnIIFeIIIFeIIIFeIIIZnII Complex

The first confacial pentaoctahedron comprised of transition metal ions namely Zn^IIFe^III_AFe^III_BFe^III_AZn^II has been synthesized by using a dinucleating nonadentate ligand. The face-sharing bridging mode enforces short Zn^II⋅⋅⋅Fe^III_A and Fe^III_A⋅⋅⋅Fe^III_B distances of 2.83 and 2.72 Å, respectively. Ab-initio CASSCF/NEVPT2 calculations provide significant negative zero-field splittings for Fe^III_A and Fe^III_B with |D_A|>|D_B| with the main component along the C₃ axis. Hence, a spin-Hamiltonian comprised of anisotropic exchange, zero-field, and Zeeman term was employed. This allowed by following the boundary conditions from the theoretical results the simulation in a theory-guided parameter determination with J^xy=+0.37, J^z=−0.32, D_A=−1.21, E_A=−0.24, D_B=−0.35, and E_B=−0.01 cm⁻¹ supported by simulations of high-field magnetic Mössbauer spectra recorded at 2 K. The weak but ferromagnetic Fe^III_AFe^III_B interaction arises from the small bridging angle of 84.8° being at the switch from anti- to ferromagnetic for the face-sharing bridging mode.     

Studies of a molecular hourglass: synthesis and magnetic characterisation of a cyclic dodecanuclear {Cr10Cu2} complex

The synthesis, structure, EPR, and magnetic studies of two dodecanuclear heterometallic cyclic clusters are reported. The compounds have the general formula [R(2)NH(2)](2)[Cr(10)Cu(2)F(14)(O(2)CCMe(3))(22)] (R=Me, 1 or iPr, 2). Both structures contain an array of metal centers which describe an approximate "hourglass", with an ammonium cation in the center of each half of the figure. The chromium sites are all six-coordinate, with the two copper sites five-coordinate. The majority of metal-metal edges are bridged by a single fluoride and two pivalate ligands, while two Cr--Cu edges are bridged by a single fluoride and a single pivalate. Magnetic studies show that 1 and 2 exhibit similar (but not identical) behavior, which can be attributed to ten antiferromagnetic and two ferromagnetic exchange interactions around the ring which gives an S=0 ground state. Quantum Monte Carlo calculations have been used to quantify the exchange interactions by successfully simulating the susceptibility for the full temperature range and thus clarifying the distinction between 1 and 2. EPR spectroscopy shows signals due to excited states, and a variable-temperature study has provided an estimate of the energy gap between the first excited state (S=1) and second excited state (S=2) for 1 that is consistent with the value obtained using the QMC method.     

Synthesis, single crystal X-ray structure and optical properties of 3,4-dimethyl-dithieno[2,3-b:3′,2′-d]thiophene-7,7-dioxide

The synthesis of the title compound (4), starting from commercial 3-bromo-4-methylthiophene, is described. The single crystal packing mode of 4, as well as the absorption and photoluminescence properties in solution and in the solid state are reported and analyzed in relation to those of the isomeric 3,5-dimethyl-dithieno[3,2-b:2′,3′-d]thiophene-4,4-dioxide (7). The different reactivities of 4 and 7 towards bromination are analyzed in the light of the results of ab initio B3LYP/6-31G^∗ calculations on both compounds.