Electronic states and pseudo Jahn-Teller distortion of heavy metal-monobenzene complexes: M(C6H6) (M = Y, La, and Lu)

Monobenzene complexes of yttrium (Y), lanthanum (La), and lutetium (Lu), M(C(6)H(6)) (M = Y, La, and Lu), were prepared in a laser-vaporization supersonic molecular beam source and studied by pulsed-field ionization zero electron kinetic energy (ZEKE) spectroscopy and ab initio calculations. The calculations included the second-order perturbation, the coupled cluster with single, double, and perturbative triple excitation, and the complete active space self-consistent field methods. Adiabatic ionization energies and metal-benzene stretching frequencies of these complexes were measured for the first time from the ZEKE spectra. Electronic states of the neutral and ion complexes and benzene ring deformation were determined by combining the spectroscopic measurements with the theoretical calculations. The ionization energies of M(C(6)H(6)) are 5.0908 (6), 4.5651 (6), and 5.5106 (6) eV, and the metal-ligand stretching frequencies of [M(C(6)H(6))](+) are 328, 295, and 270 cm(-1) for M = Y, La, and Lu, respectively. The ground states of M(C(6)H(6)) and [M(C(6)H(6))](+) are (2)A(1) and (1)A(1), respectively, and their molecular structures are in C(2v) point group with a bent benzene ring. The deformation of the benzene ring upon metal coordination is caused by the pseudo Jahn-Teller interaction of (1(2)E(2)+1(2)A(1)+2(2)E(2)) e(2) at C(6v) symmetry. In addition, the study shows that spectroscopic behaviors of Y(C(6)H(6)) and La(C(6)H(6)) are similar to each other, but different from that of Lu(C(6)H(6)).     

The Finite Hankel Transform Operator: Some Explicit and Local Estimates of the Eigenfunctions and Eigenvalues Decay Rates

For fixed real numbers \(c>0,\)\(\alpha >-\frac{1}{2},\) the finite Hankel transform operator, denoted by \(\mathcal {H}_c^{\alpha }\) is given by the integral operator defined on \(L^2(0,1)\) with kernel \(K_{\alpha }(x,y)= \sqrt{c xy} J_{\alpha }(cxy).\) To the operator \(\mathcal {H}_c^{\alpha },\) we associate a positive, self-adjoint compact integral operator \(\mathcal Q_c^{\alpha }=c\, \mathcal {H}_c^{\alpha }\, \mathcal {H}_c^{\alpha }.\) Note that the integral operators \(\mathcal {H}_c^{\alpha }\) and \(\mathcal Q_c^{\alpha }\) commute with a Sturm-Liouville differential operator \(\mathcal D_c^{\alpha }.\) In this paper, we first give some useful estimates and bounds of the eigenfunctions \(\varphi ^{(\alpha )}_{n,c}\) of \(\mathcal H_c^{\alpha }\) or \(\mathcal Q_c^{\alpha }.\) These estimates and bounds are obtained by using some special techniques from the theory of Sturm-Liouville operators, that we apply to the differential operator \(\mathcal D_c^{\alpha }.\) If \((\mu _{n,\alpha }(c))_n\) and \(\lambda _{n,\alpha }(c)=c\, |\mu _{n,\alpha }(c)|^2\) denote the infinite and countable sequence of the eigenvalues of the operators \(\mathcal {H}_c^{(\alpha )}\) and \(\mathcal Q_c^{\alpha },\) arranged in the decreasing order of their magnitude, then we show an unexpected result that for a given integer \(n\ge 0,\)\(\lambda _{n,\alpha }(c)\) is decreasing with respect to the parameter \(\alpha .\) As a consequence, we show that for \(\alpha \ge \frac{1}{2},\) the \(\lambda _{n,\alpha }(c)\) and the \(\mu _{n,\alpha }(c)\) have a super-exponential decay rate. Also, we give a lower decay rate of these eigenvalues. As it will be seen, the previous results are essential tools for the analysis of a spectral approximation scheme based on the eigenfunctions of the finite Hankel transform operator. Some numerical examples will be provided to illustrate the results of this work.     

Connection relations and bilinear formulas for the classical orthogonal polynomials

Suppose we have an operator T that maps a set of orthogonal polynomials {P_n(x)}_{n = o}^∞ to another set of orthogonal polynomials. We show how such a mapping can be used to derive connection relations as well as bilinear formulas for the pre-images {P_n(x)}_{n = o}^∞. This method is carried out in detail for the Jacobi, Laguerre, and Hahn polynomials.     

Kinetics of adsorption of zinc-ions by doped manganese dioxides

Using⁶⁵Zn-labelled solutions, the kinetics of the specific adsorption of Zn²⁺-ions by doped manganese dioxides was studied, at pH values corresponding to their isoelectric points (IEP's), by γ-ray scintillation counting. The rate of the fast adsorption of Zn²⁺-ions by doped dioxides increased in the series: Li⁺-doped<undoped<Mo(VI)-≈V(V)-doped samples. The uptake of Zn²⁺-ions in about 10 minutes exhibited a similar increase. Compared to the undoped sample, the extent and the rate of adsorption were lower for the samples doped with an ion of valence<4 but were higher for samples doped with ions of valence>4.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Dendrimers with a copper(I) bis(phenanthroline) core: synthesis, electronic properties, and kinetics

The copper(I) bis(chelate) complex Cu(L(0))(2) has been prepared from 2,9-diphenethyl-1,10-phenanthroline and Cu(CH(3)CN)(4)BF(4). Derivative Cu(L(0))(2) has been characterized by NMR, UV-vis spectroscopy, and X-ray crystallography. Interestingly, owing to the presence of the ethylene linker, the interligand pi-pi stacking interactions between the phenyl rings and the phenanthroline subunits in Cu(L(0))(2) do not induce significant distortions of the pseudotetrahedral symmetry around the Cu(I) center in the solid state or in solution. Following the synthesis of Cu(L(0))(2), dendrimers Cu(L(1)(-)(4))(2) with a Cu(I) bis(2,9-diphenethyl-1,10-phenanthroline) core surrounded by Fréchet type dendritic branches have been prepared and the kinetics of their cyanide-assisted demetalation studied. Importantly, the surrounding dendritic wedges have no significant influence on the coordination geometry of the Cu(I) center, as deduced from their absorption spectra. Therefore, the variations of the rate constants only reflect changes resulting from the presence of the dendritic branches. The kinetics of the cyanide-mediated demetalation reaction indeed revealed that cyanide diffusion through the dendritic shell is slightly influenced by the size of the branches. Significant effects were observed in the kinetics when going from the third to the fourth generation and have been ascribed to changes in the lipophilicity around the metallic core as a result of dendritic encapsulation.     

Synthesis of some derivatives of imidazo[1,2-a]pyridine,pyrazolo[1,5-b]imidazole,and 4-(3H)quinazolinone from α-ketohydrazidoyl bromides

α-Aroyl-N-arylhydrazidoyl bromides 1 react with 2-aminopyridine in ethanol and give 2-aryl-3-arylazo-imidazo[1,2-α]pyridines 2 in 60-75% yield. The reaction of 1 with 3-phenyl-5-aminopyrazole in ethanol leads to 2,6-diaryl-3-arylazo-1H-pyrazolo[1,5-b]imidazoles 3 in almost quantitative yield. Also, 1 react with anthran-ilic acid in the presence of triethylamine giving 3-arylamino-2-aroyl-4-(3H)quinazolinones 4 in 80-85% yield. The structures of the products were assigned and confirmed on the basis of their elemental analysis and electronic absorption, infrared and nmr spectra.     

Cooperative recognition of C60-ammonium substrates by a ditopic oligophenylenevinylene/crown ether host

A new fullerene derivative with an ammonium subunit has been prepared. Its ability to form supramolecular complexes with oligophenylenevinylene derivatives bearing one or two crown ether moieties has been evidenced by electrospray mass spectrometry, and UV-visible and luminescence spectroscopy experiments. Interestingly, the assembly of the C60-ammonium cation with the oligophenylenevinylene derivative bearing two crown ether moieties leads to the cooperative formation of the 2:1 complex owing to intramolecular fullerene-fullerene interactions.     

Supramolecular click chemistry for the self-assembly of a stable Zn(II)-porphyrin-C60 conjugate

Owing to the complementarity between a bis-Zn(II)-porphyrin receptor and a fullerene ligand bearing two pyridine substituents, the substrate can be clicked onto the ditopic receptor, thus leading to a stable non-covalent macrocyclic 1 ratio 1 complex.