Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

We report a detailed physical analysis on a family of isolated, antiferro-magnetically (AF) coupled, chromium(III) finite chains, of general formula (Cr(RCO(2))(2)F)(n) where the chain length n = 6 or 7. Additionally, the chains are capped with a selection of possible terminating ligands, including hfac (= l,l,l,5,5,5-hexafluoropentane-2,4-dionate(l-)), acac (= pentane-2,4-dionate(l-)) or (F)(3). Measurements by inelastic neutron scattering (INS), magnetometery and electron paramagnetic resonance (EPR) spectroscopy have been used to study how the electronic properties are affected by n and capping ligand type. These comparisons allowed the subtle electronic effects the choice of capping ligand makes for odd member spin 3/2 ground state and even membered spin 0 ground state chains to be investigated. For this investigation full characterisation of physical properties have been performed with spin Hamiltonian parameterisation, including the determination of Heisenberg exchange coupling constants and single ion axial and rhombic anisotropy. We reveal how the quantum spin energy levels of odd or even membered chains can be modified by the type of capping ligand terminating the chain. Choice of capping ligands enables Cr-Cr exchange coupling to be adjusted by 0, 4 or 24%, relative to Cr-Cr exchange coupling within the body of the chain, by the substitution of hfac, acac or (F)(3) capping ligands to the ends of the chain, respectively. The manipulation of quantum spin levels via ligands which play no role in super-exchange, is of general interest to the practise of spin Hamilton modelling, where such second order effects are generally not considered of relevance to magnetic properties.     

Influencing the nuclearity and constitution of heterometallic rings via templates

Heterometallic wheels can be templated about tertiary amines and imidazoles, leading to new octa-, nona- and deca-nuclear rings.     

A new class of generalized close-to-starlike functions defined by the Srivastava-Attiya operator

In this paper, we consider a new class CS*s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function Φ(z, s, a). Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.     

No‐go result for supersymmetric gauge theories in the causal approach

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non‐Abelian gauge theory (SUSY‐QCD) is uniquely determined by some natural assumptions, as in the case of Yang‐Mills models. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.     

Magnetic circular dichroism spectroscopy of antiferromagnetically coupled hetero-metallic rings [H2NR2][Cr7MF8(O2CCMe3)16

The optical and magnetic properties of the multi-metal rings [NH(2)R(2)][Cr(7)MF(8)(O(2)CCMe(3))(16)], where M = Cd(II), Mn(II) or Ni(II), have been studied using variable-field and variable-temperature magnetic circular dichroism (MCD) in the UV-visible spectra. Spectra of samples were recorded in a frozen organic matrix or cast in a polymethacrylate (PMMA) polymer film between 1.7 and 75 K. The spectra are characteristic of the Cr(III) ion (d(3)) in a rhombic field when M = Cd(II). In the case that M = Ni(II) additional optical transitions arise from the d(8) ion whereas for M = Mn(II) no additional transitions are observed. The influence of magnetic exchange is apparent from a change in the sign of the MCD signal between complexes in which the hetero-atom has a local spin moment greater, or less, than that of Cr(III), S = 3/2, namely, Mn(II), S = 5/2, and Ni(II), S = 1. The exchange coupling generates a manifold of thermally accessible electronic states that give rise to variations in MCD intensity as well as additional spectral features as the temperature is raised. Equations have been derived to relate the splittings observed in the optical spectrum to the single-ion ground state zero-field splittings of chromium(III). There is reasonable agreement between the sign and magnitude of the contribution to the cluster anisotropy from that of the single ion with values estimated from other techniques.     

Studies of finite molecular chains: synthesis, structural, magnetic and inelastic neutron scattering studies of hexa- and heptanuclear chromium horseshoes

We report the synthesis and structural characterisation of a family of finite molecular chains, specifically [{[R(2)NH(2)](3)[Cr(6)F(11)(O(2)CCMe(3))(10)]}(2)] (in which R=nPr 1, Et 2, nBu 3), [{Et(2)NH}(2){[Et(2)NH(2)](3)[Cr(7)F(12)(O(2)CCMe(3))(12)][HO(2)CCMe(3)](2)}(2)] (4), [{[Me(2)NH(2)](3)[Cr(6)F(11)(O(2)CCMe(3))(10)]2.5 H(2)O}(4)] (5) and [{[iPr(2)NH(2)](3)[Cr(7)F(12)(O(2)CCMe(3))(12)]}(2)] (6). The structures all contain horseshoes of chromium centres, with each Cr...Cr contact within the horseshoe bridged by a fluoride and two pivalates. The horseshoes are linked through hydrogen bonds to the secondary ammonium cations in the structure, leading to di- and tetra-horseshoe structures. Through magnetic measurements and inelastic neutron scattering studies we have determined the exchange coupling constants in 1 and 6. In 1 it is possible to distinguish two exchange interactions, J(A)=-1.1 meV and J(B)=-1.4 meV; J(A) is the exchange interactions at the tips of the horseshoe and J(B) is the exchange within the body of the horseshoe (1 meV=8.066 cm(-1)). For 6 only one interaction was needed to model the data: J=-1.18 meV. The single-ion anisotropy parameters for Cr(III) were also derived for the two compounds as: for 1, D(Cr)=-0.028 meV and |E(Cr)|=0.005 meV; for 6, D(Cr)=-0.031 meV. Magnetic-field-dependent inelastic neutron scattering experiments on 1 allowed the Zeeman splitting of the first two excited states and level crossings to be observed. For the tetramer of horseshoes (5), quantum Monte Carlo calculations were used to fit the magnetic susceptibility behaviour, giving two exchange interactions within the horseshoe (-1.32 and -1.65 meV) and a weak inter-horseshoe coupling of +0.12 meV. Multi-frequency variable-temperature EPR studies on 1, 2 and 6 have also been performed, allowing further characterisation of the spin Hamiltonian parameters of these chains.