Thermal Decomposition of Hydrated Lanthanide Picrates by TG/DTG and DSC Analyses

Hydrated lanthanide picrates with a composition of: Ln(pic)₃⋅xH₂O (Ln=La–Lu, Y) were synthesized and characterized. Thermal decomposition of the picrates by TG/DTG and DSC techniques are reported. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis and physical properties of K4[Fe(C5O5)2(H2O)2](HC5O5)2·4H2O (C5O5(2-) = croconate): a rare example of ferromagnetic coupling via H-bonds

The reaction of the croconate dianion (C(5)O(5))(2-) with a Fe(III) salt has led, unexpectedly, to the formation of the first example of a discrete Fe(II)-croconate complex without additional coligands, K(4)[Fe(C(5)O(5))(2)(H(2)O)(2)](HC(5)O(5))(2)·4H(2)O (1). 1 crystallizes in the monoclinic P2(1)/c space group and presents discrete octahedral Fe(II) complexes coordinated by two chelating C(5)O(5)(2-) anions in the equatorial plane and two trans axial water molecules. The structure can be viewed as formed by alternating layers of trans-diaquabis(croconato)ferrate(II) complexes and layers containing the monoprotonated croconate anions, HC(5)O(5)(-), and noncoordinated water molecules. Both kinds of layers are directly connected through a hydrogen bond between an oxygen atom of the coordinated dianion and the protonated oxygen atom of the noncoordinated croconate monoanion. A H-bond network is also formed between the coordinated water molecule and one oxygen atom of the coordinated croconate. This H-bond can be classified as strong-moderate being the O···O bond distance (2.771(2) ?) typical of moderate H-bonds and the O-H···O bond angle (174(3)°) typical of strong ones. This H-bond interaction leads to a quadratic regular layer where each [Fe(C(5)O(5))(2)(H(2)O)(2)](2-) anion is connected to its four neighbors in the plane through four equivalent H-bonds. From the magnetic point of view, these connections lead to an S = 2 quadratic layer. The magnetic properties of 1 have been reproduced with a 2D square lattice model for S = 2 ions with g = 2.027(2) and J = 4.59(3) cm(-1). This model reproduces quite satisfactorily its magnetic properties but only above the maximum. A better fit is obtained by considering an additional antiferromagnetic weak interlayer coupling constant (j) through a molecular field approximation with g = 2.071(7), J = 2.94(7) cm(-1), and j = -0.045(2) cm(-1) (the Hamiltonian is written as H = -JS(i)S(j)). Although this second model might still be improved since there is also an extra contribution due to the presence of ZFS in the Fe(II) ions, it confirms the presence of weak ferromagnetic Fe-Fe interactions through H-bonds in compound 1 which represents one of the rare examples of ferromagnetic coupling via H-bonds.     

On the pure critical exponent problem for the p-Laplacian

In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the $p$ -Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology and discrete symmetry. Pioneering works related to the case $p=2$ are Brezis and Nirenberg (Comm Pure Appl Math 36, 437–477, 1983), Coron (C R Acad Sci Paris Sr I Math 299, 209–212, 1984), and Bahri and Coron (Comm. Pure Appl. Math. 41, 253–294, 1988). A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries.     

Synthesis, Characterization, and Crystal Structures of New Dications Bearing the -Se-Se- Bridge

Starting from 1,3-dimethyl-4-imidazoline-2-selone (1), 1,2-bis(2-selenoxo-3-methyl-4-imidazolinyl-2-)ethane (3) and 1,3-dimethylimidazolidine-2-selone (4), the following six compounds, [(C(5)H(8)N(2)Se-)(2)](2+).2Br(-) (I), [(C(5)H(8)N(2)Se-)(2)](2+).2I(-) (II), [(C(5)H(8)N(2)Se-)(2)](2+).Cl(-).I(3)(-) (III) [(C(5)H(10)N(2)Se-)(2)](2+).Br(-).IBr(2)(-) (IV), [(C(5)H(7)N(2)Se-)(2)](2+).I(3)(-).(1)/(2)I(4)(-) (V) and [(C(5)H(7)N(2)Se-)(2)](2+).2I(-).CH(3)CN (VI), in which the selenium compounds are oxidized to dications bearing the uncommon -Se-Se- bridge, have been prepared, and I-V crystallographically characterized. I and III were obtained by reacting 1 with IBr and ICl respectively, while II was obtained by reduction of previously described hypervalent selenium compound of 1 (5) bearing the I-Se-I group with elemental tellurium. These three compounds contain the same [(C(5)H(8)N(2)Se-)(2)](2+) dication balanced by two bromides in I, two iodides in II, and Cl(-) and I(3)(-) in III. However, on the basis of the Se-Cl bond length of 2.778(5) ?, III can also be considered as formed by the [(C(5)H(8)N(2)Se-)(2)Cl](+) cation, with I(3)(-) as counterion. Similarly to III, compound IV, which was obtained by reacting 4 with IBr, can be considered as formed by [(C(5)H(10)N(2)Se-)(2)Br](+) cations and IBr(2)(-) anions. As in II, compound V has been prepared by reduction of the hypervalent selenium compound of 3 (6) bearing two I-Se-I groups with elemental tellurium. In V, the [(C(5)H(7)N(2)Se-)(2)](2+) cation is balanced by I(3)(-) and half I(4)(2-) anions. The structural data show that all the cations are very similar, with Se-Se bond lengths ranging from 2.409(2) to 2.440(2) ?. FT-IR and FT-Raman spectra of I-VI allow one to identify two bands around 230 +/- 10 and 193 +/- 5 cm(-1) that are common to all compounds. These bands are generally strong in the FT-Raman and weak in the FT-IR spectra and should contain a contribution of the nu(Se-Se) stretching vibration. The spectra are also in good agreement with the structural features of the polyhalide anions present in the crystals. Crystallographic data are as follows: I is monoclinic, space group P2(1), with a = 9.849(6) ?, b = 11.298(5) ?, c = 7.862(6) ?, beta = 106.44(2) degrees, Z = 2, and R = 0.0362; II is monoclinic, space group P2(1), with a = 8.063(6) ?, b = 11.535(5) ?, c = 10.280(5) ?, beta = 107.13(2) degrees, Z = 2, and R = 0.0429, III is monoclinic, space group P2(1)/n, with a = 10.431(7) ?, b = 18.073(5) ?, c = 11.223(6) ?, beta = 100.76(2) degrees, Z = 4, and R = 0.0490; IV is monoclinic, space group P2(1)/n, with a = 10.298(5) ?, b = 18.428(7) ?, c = 11.475(6) ?, beta = 104.10(4) degrees, Z = 4, and R = 0.0300; V is triclinic, space group P&onemacr;, with a = 7.456(6) ?, b = 11.988(5) ?, c = 12.508(5) ?, alpha = 79.32(2) degrees, beta = 85.49(2) degrees, gamma = 80.62(2) degrees, Z = 2, and R = 0.0340.     

Some partition and analytical identities arising from the Alladi,Andrews, Gordon bijection

The Ramanujan Journal - In the work of Alladi et al. (J Algebra 174:636–658, 1995) the authors provided a generalization of the two Capparelli identities involving certain classes of integer...