Synthesis and characterization of manganese(II) and iron(III) d5 tripodal imidazole complexes. Effect of oxidation state, protonation state and ligand conformation on coordination number and spin state

The 1 : 3 Schiff base condensates of tris(2-aminoethyl)amine (tren) or tris(3-aminopropyl)amine (trpn) with 4-methyl-5-imidazolecarboxaldehyde, H3L1 and H3L2, respectively, were generated in situ and used to prepare complexes with manganese(II) and iron(III). The resultant complexes, [MnH3L1](ClO4)2, [MnH3L1](ClO4)2.EtOH.H2O, [MnH3L2](ClO4)2, [FeH3L1](ClO4)3.1.5(EtOH) and [FeHL1](I3) (0.525)(I)(0.475).2.625H2O, have been characterized by EA, IR, ES MS, variable temperature magnetic susceptibility, X-ray crystallography, and M?ssbauer spectroscopy for the iron complexes. The three manganese(II) complexes are high spin with [MnH3L2](ClO4)2 exhibiting coordination number seven while the others are six coordinate. [FeH3L1](ClO4)3.1.5(EtOH) has two iron sites, a seven coordinate and a pseudo seven coordinate site. The complex is high spin at room temperature but exhibits a magnetic moment that decreases with temperature corresponding to conversion of one of the sites to low spin. [FeHL1](I3) (0.525)(I)(0.475).2.625H2O is low spin even at room temperature. In the present complexes the apical nitrogen atom, N(ap), of the tripodal ligand is pyramidal and directed toward the metal atom. The data show that the M-N(ap) distance decreases as the oxidation state of the metal increases, as the number of bound imidazole protons on the ligand increases, and as the number of carbon atoms in the backbone of the ligand (tren vs. trpn) increases. In a limiting sense, short M-N(ap) distances result in high spin seven coordinate mono capped octahedral complexes and long M-N(ap) distances result in low spin six coordinate octahedral complexes.     

Harmonic Green's functions for flexural waves in semi-infinite plates with arbitrary boundary conditions and high-frequency approximation for convex polygonal plates

This paper provides a method for obtaining the harmonic Green's function for flexural waves in semi-infinite plates with arbitrary boundary conditions and a high frequency approximation of the Green's function in the case of convex polygonal plates, by using a generalised image source method. The classical image source method consists in describing the response of a point-driven polygonal plate as a superposition of contributions from the original source and virtual sources located outside of the plate, which represent successive reflections on the boundaries. The proposed approach extends the image source method to plates including boundaries that induce coupling between propagating and evanescent components of the field and on which reflection depends on the angle of incidence. This is achieved by writing the original source as a Fourier transform representing a continuous sum of propagating and evanescent plane waves incident on the boundaries. Thus, the image source contributions arise as continuous sums of reflected plane waves. For semi-infinite plates, the exact Green's function is obtained for an arbitrary set of boundary conditions. For polygonal plates, a high-frequency approximation of the Green's function is obtained by neglecting evanescent waves for the second and subsequent reflections on the edges. The method is compared to exact and finite element solutions and evaluated in terms of its frequency range of applicability.