Mass‐lumping or not mass‐lumping for eigenvalue problems

In this article we analyze the effect of mass‐lumping in the linear triangular finite element approximation of second‐order elliptic eigenvalue problems. We prove that the eigenvalue obtained by using mass‐lumping is always below the one obtained with exact integration. For singular eigenfunctions, as those arising in non convex polygons, we prove that the eigenvalue obtained with mass‐lumping is above the exact eigenvalue when the mesh size is small enough. So, we conclude that the use of mass‐lumping is convenient in the singular case. When the eigenfunction is smooth several numerical experiments suggest that the eigenvalue computed with mass‐lumping is below the exact one if the mesh is not too coarse. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 653–664, 2003     

Intermolecular proton transfer in solid phase: a rare example of crystal-to-crystal transformation from hydroxo- to oxo-bridged iron(III) molecule-based magnet

Intermolecular proton transfer in solid phase from the hydroxo bridge to a water molecule occurs in a new mu-hydroxo iron(III) compound of formula {EtNH3[Fe2(ox)2Cl2(mu-OH)].2H2O}n leading to a still crystalline compound in which the mu-oxo bridge replaces the mu-hydroxo one. Both three-dimensional compounds exhibit magnetic ordering at Tc ca. 70 K due to a spin canting.     

Novel chiral three-dimensional iron(III) compound exhibiting magnetic ordering at T(c) = 40 K

The preparation and crystal structure determination of the iron(III) compound of formula [(NH(4))(2)[Fe(2)O(ox)(2)Cl(2)].2H(2)O](n) (1) (ox = oxalate dianion) are reported here. Complex 1 crystallizes in the orthorhombic system, space group Fdd2, with a = 14.956(7) A, b = 23.671(9) A, c = 9.026(4) A, and Z = 8. The structure of complex 1 consists of the chiral anionic three-dimensional network [Fe(2)O(ox)(2)Cl(2)](2-) where the iron(III) ions are connected by single oxo and bisbidentate oxalato groups. The metal-metal separations through these bridging ligands are 3.384(2) and 5.496(2) A, respectively. Ammonium cations and crystallization water molecules are located in the helical pseudohexagonal tunnels defined by iron atoms. The longest iron-iron distance in the pseudohexagonal tunnel is 15.778(2) A whereas the shortest one is 8.734(2) A. The iron atoms are hexacoordinated: a terminal chloro ligand and five oxygen atoms, that of the oxo group and four from two cis coordinated oxalate ligands, build a distorted octahedral environment around the metal atom. The Fe-O(oxo) bond distance [1.825(2) A] is significantly shorter than the Fe(III)-O(ox) [average value 2.103(4) A] and Fe(III)-Cl bond distances [2.314(2) A]. Magnetic susceptibility measurements of 1 in the temperature range 2.0-300 K reveal the occurrence of a susceptibility maximum at 195 K and a transition toward a magnetically ordered state in the lower temperature region with T(c) = 40 K. The strong antiferromagnetic coupling through the oxo bridge (J = -46.4 cm(-1), the Hamiltonian being H = -JS(A).S(B)) accounts for the susceptibility maximum whereas a weak spin canting of approximately 0.3 degrees due to the antisymmetric magnetic exchange within the chiral three-dimensional network is responsible for the magnetic ordering. The values of coercive field (H(c)) and remnant magnetization (M(r)) obtained from the hysteresis loop of 1 at 5 K are 4000 G and 0.016 micro(B).     

Fragmentation energetics of the phenol(+)···Ar(3) cation cluster

The various dissociation thresholds of phenol(+)···Ar(3) complexes for the consecutive loss of all three Ar ligands were measured in a molecular beam using resonant photoionization efficiency and mass analyzed threshold ionization spectroscopy via excitation of the first excited singlet state (S(1)). The adiabatic ionization energy is derived as 68077 ± 15 cm(-1). The analysis of the dissociation thresholds demonstrate that all three Ar ligands in the neutral phenol···Ar(3) tetramer are attached to the aromatic ring via π-bonding, denoted phenol···Ar(3)(3π). The value of the dissociation threshold for the loss of one Ar ligand from phenol(+)···Ar(3)(3π), ～190 cm(-1), is significantly lower than the binding energy measured for the π-bonded Ar ligand in the phenol(+)···Ar(π) dimer, D(0) = 535 ± 3 cm(-1). This difference is rationalized by an ionization-induced π → H isomerization process occurring prior to dissociation, that is, one Ar atom in phenol(+)···Ar(3)(3π) moves to the OH binding site, leading to a structure with one H-bonded and 2 π-bonded ligands, denoted phenol(+)···Ar(3)(H/2π). The dissociation thresholds for the loss of two and three Ar atoms are also reported as 860 and 1730 cm(-1). From these values, the binding energy of the H-bound Ar atom can be estimated as 870 cm(-1).     

Textural and calorimetric investigations on a homologous series of mesogenic azocompounds complexed with palladium(II)

A comparative study of some mesogenic azobenzene compounds and their organometallic palladium(II) derivatives is reported. On the basis of the textural properties, calorimetric data and uniaxial order parameters (as deduced approximately from infrared spectroscopy), the main features induced by palladium complexation are (i) the transition temperatures increase, (ii) the number of ordered mesophases increases, (iii) the nematic uniaxial order parameter decreases, (iv) the textures are typical of highly ordered phases, and (v) an optical biaxiality appears in the nematic phase. The calorimetric data as well as the order parameters, if discussed in terms of molecular biaxiality result are interpreted at least qualitatively. Optical investigations show that macroscopical biaxial ordering can be achieved.     

Very long-distance magnetic coupling in a dicopper(II) metallacyclophane with extended π-conjugated diphenylethyne bridges

Self-assembly of the rigid rodlike ligand N,N'-4,4'-diphenylethynebis(oxamate) (dpeba) and Cu(2+) ions affords a novel dinuclear copper(II) metallacyclophane (nBu(4)N)(4)[Cu(2)(dpeba)(2)]·4MeOH·2Et(2)O (1) featuring a very long intermetallic distance (r = 15.0 ?). Magnetic susceptibility measurements for 1 reveal a moderately weak but nonnegligible intramolecular antiferromagnetic coupling between the two metal centers across the double para-substituted diphenylethynediamidate bridge (J = -3.9 cm(-1); H = -JS(1)S(2), where S(1) = S(2) = S(Cu) = (1)/(2)). Density functional electronic structure calculations on 1 support the occurrence of a spin polarization mechanism.