Transverse susceptibility as the low-frequency limit of ferromagnetic resonance

A new theory of transverse susceptibility (TS) based on magnetization vector dynamics, as described by the Landau–Lifshitz equation of motion, is given. It is shown that the traditional TS experiment is, in fact, the zero-frequency limit of the ferromagnetic resonance (FMR). The importance of these results resides in the generality of the approach which allows one to find the TS for virtually any magnetic system if an expression for the magnetic free-energy density is known. Moreover, the effect of the frequency of excitatory AC field on the TS experiments and the effect of energy dissipation through the imaginary part of TS emerge coherently from the new TS model.     

Mechanism of ferromagnetic coupling in copper(II)-gadolinium(III) complexes

This paper offers the first series of state-of-the-art quantum chemical calculations (CASSCF, CASPT2, MS-CASPT2) and analytical models for the well-known problem of quasi-general ferromagnetic coupling in copper-gadolinium complexes. A system chosen from the chemical report of Costes et al. was taken as prototype. At the CASSCF level, calculated results for the experimental structure reproduced the magnetic coupling constant well (J(calcd)( )()= +7.67 cm(-)(1) vs J(exp)( )()= +7.0 cm(-)(1)). For more insight, the study molecule was further idealized by geometry optimization to C(2)(v)() symmetry. Systematic ab initio computation experiments were designed and performed. Owing to specific problems related to the non-aufbau ground configuration of the [CuL-Gd] complexes, the calculations were conducted in a nonstandard manner. We found that the qualitative mechanism of Kahn, assigned to the electron jump from 3d of Cu(II) to 5d shell of Gd(III), can be presented effectively as the cause of the phenomenon, if CASPT2 MOs are taken as magnetic orbitals. We showed that the ferromagnetic coupling is also matched and magnified by spin polarization effects over the ligand, in line with the early assumption of Gatteschi. To be distinguished from the initial hypothesis of Gatteschi, which assumed the role of 6s AO of Gd(III), we found that one 5d-type AO is actually involved in the polarization scheme. In fact, the Gatteschi and Kahn mechanisms are not mutually contradictory, but are even interconvertible with appropriate changes of the magnetic orbitals. Within C(2)(v)() symmetry of complexes, the ferromagnetic coupling can be qualitatively regarded as the preponderant influence of interaction channels exhibiting orbital orthogonality (four 3d-4f contacts) over the nonorthogonal ones (two 3d-4f contacts). The effective preponderance from ferromagnetic pathways is supported by CASPT2 results. One may explain the generality of Cu(II)-Gd(III) ferromagnetic coupling as being correlated with the large occurrence of approximate pseudo-C(2)(v)() geometry of complexes. The observed orbital regularity is lost in lower symmetries. Thus, the antiferromagnetic exceptions occur when the molecular asymmetry is advanced (e.g., owing to strong chemical nonequivalence of the donor atoms).     

New synthetic and structural aspects in the chemistry of alkylaluminum fluorides. The mutual influence of hard and soft ligands and the hybridization as rigorous structural criterion

A general synthetic strategy starting from metal alkyls is reported based on the hydrogen difluoride anion as a suitable reagent for obtaining organometallic fluorides. The newly prepared compounds are [Me(4)N][(i-Bu)(2)AlF(2)] (1), [Ph(4)P][(i-Bu)(2)AlF(2)] (2), and [Ph(4)P][AlF(4)] (3), containing the tetrahedral anions [(i-Bu)(2)AlF(2)](-) and [AlF(4)](-). The actual structures are prototypes that allowed a comparison of inorganic and organometallic fluorides in the frame of the hard and soft acid and base principle, by means of ab initio calculations. A new theoretical model is designed to put in equation form the qualitative statements of the Bent rule. The model allows the rationalization of the tendencies of bond angle variation in [R(2)MX(2)] systems containing a main group metal (M), in terms of hybridization of the central atom and the reciprocal influence of hard and soft ligands.     

Syntheses, structures, and surface aromaticity of the new carbaalane [(AlH)(6)(AlNMe(3))(2)(CCH(2)R)(6)] (R = Ph, CH(2)SiMe(3)) and a stepwise functionalization of the inner and outer sphere of the cluster

The reaction of the acetylene RC triple bond CH (R = Ph, CH(2)SiMe(3)) with an excess of AlH(3).NMe(3) in boiling toluene leads to the carbaalane [(AlH)(6)(AlNMe(3))(2)(CCH(2)R)(6)] (R = Ph 1, CH(2)SiMe(3) 2) in good yield. Treatment of 2 with BCl(3) under varying conditions gives the chlorinated products [(AlCl)(6)(AlNMe(3))(2)(CCH(2)CH(2)SiMe(3))(6)] 3 and [(AlCl)(6)(AlNMe(3))(2)(CCH(2)CH(2)SiMe(2)Cl)(6)] 4, respectively. The latter clearly demonstrates that the cluster can be stepwise functionalized within the inner and outer sphere. The X-ray single-crystal structures of 1, 2, and 4 have been determined. All compounds have in common that the central core consists of a cluster having eight aluminum and six carbon atoms. The bonding properties in this cluster are described as a new manifestation of three-dimensional surface aromaticity. Each Al(4)C fragment of the cube is formed by four bonds with three electron pairs, thus leading to a strong delocalization of the electrons. A phenomenological modeling using a three-dimensional Hückel scheme with fitted parameters to reproduce the energies from ab initio calculations revealed that the orbital scheme localized at one Al(4)C fragment possesses an orbital sextet with a large HOMO-LUMO gap. This is in line with the criteria of aromaticity. The idea of aromaticity was sustained also by qualitative valence bond reasons enumerating the different resonance structures by means of graph theoretical methods.     

The Density Functional Theory Account of Interplaying Long-Range Exchange and Dispersion Effects in Supramolecular Assemblies of Aromatic Hydrocarbons with Spin

Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds.     

Polymers from a levopimaric acid–acrylonitrile Diels–Alder adduct: Synthesis and characterization

The Diels–Alder adduct of levopimaric acid with acrylonitrile was efficiently prepared from resin acids. Excellent addition reaction yields (ca. 95%) were obtained. The adduct was converted into polyamides by polycondensation with diamines. When the same adduct was subjected to a dehydrodecarboxylation reaction, a novel ketone dinitrile derivative was obtained. This trifunctional product was also converted into polyamides by polycondensation with diamines. When the ketone dinitrile was hydrolyzed in the presence of alkalies and the reaction product was chlorinated, a ketone diacid chloride was obtained. A polyester was synthesized by the polycondensation of the diacid chloride with a diol. The structures of the Diels–Alder adduct, ketone dinitrile derivative, ketone diacid chloride, and polymers were established by means of elemental analysis, IR and NMR spectroscopy, and molecular weight determinations. Both the polyamides and the polyester were low‐molecular‐weight polymers soluble in polar solvents. The thermal behavior of the monomers and polymers was evaluated by thermogravimetric analysis. The thermal studies showed that the polymers were fairly thermostable substances, except the polyester, which appeared to be a substance with good thermal stability. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6308–6322, 2005     

Rationalization of the lanthanide-ion-driven magnetic properties in a series of 4f-5d cyano-bridged chains

Magnetic properties of new d-f cyanido-bridged 1D assemblies [RE(pzam)(3)(H(2)O)W(CN)(8)]·H(2)O (RE(III) = Gd, 1, Tb, 2, Dy, 3; pzam = pyrazine-2-carboxamide) were studied by temperature- and field-dependent magnetization measurements. No evidence for 3D interchain magnetic ordering is found above 2 K. Multiconfiguration ab initio calculations and subsequent modeling afforded simulation of the weak zero-field splitting effect in 1 and discussion of magnetic anisotropy in the f units of compounds 2 and 3. A semiquantitative corroboration with the experimental magnetic measurements is presented, performing the simulation of magnetic susceptibility vs temperature and magnetization vs field variation. The association into molecular and supramolecular architectures is analyzed by means of energy decomposition subsequent to the DFT calculations on idealized molecular models extracted from the experimental chain structure.     

DFT study of structure–properties correlations in [MnTPP][TCNE] quasi-one-dimensional molecular magnets

We report the first band structure calculations of the quasi-one-dimensional [MnTPP][TCNE] compounds (TPP = meso-tetraphenylporphyrinato, TCNE = tetracyanoethylene), based on Density Functional Theory (DFT) methods, in order to interpret the magnetic ordering in these prototypic systems. We compare and contrast the results of broken-symmetry DFT calculations for extended systems, with periodic boundary conditions, and for finite systems, magnetic dimers modeling the actual molecular magnets. By varying systematically the main angles, we are able to determine the geometry dependence of the exchange interaction. Structure–properties correlations in these charge-transfer salts reveal the determinant role of the Mn-(N≡C)_TCNE bond angle on the strength of the ferrimagnetic coupling between the S ₁ = 2 spin located on the Mn^III-porphyrin donor and the S ₂ = 1/2 spin positioned on the cyanocarbon acceptor. When the Mn-(N≡C)_TCNE angle is decreased, the intrachain magnetic coupling strengthens, correlated with the increase in the d_z² - p* d_{{z^{2} }} - \pi * orbital overlap. The exchange coupling constants resulting from DFT calculations of extended systems, with periodic boundary conditions, were found to be consistent with those obtained for the dimers, but systematically smaller. The exchange constants vary strongly with the functional used, hybrid functionals such as B3LYP leading to results that better correlate with the experimental mean-field critical temperatures. The coupling constant varies significantly with the type of broken-symmetry approach, depending on the overlap between magnetic orbitals, but weakly on the basis set once polarization effects are included. The electronic structure calculations for the extended systems provide a density of states consistent with the energy spectrum of the corresponding dimer, allowing for an intuitive explanation of the intrachain ferrimagnetic ordering.