Diophantine inequalities involving several power sums

Let denote the ring of power sums, i.e. complex functions of the form for some and _iA, where is a multiplicative semigroup. Moreover, let We consider Diophantine inequalities of the form where >1 is a quantity depending on the dominant roots of the power sums appearing as coefficients in F(n,y), and show that all its solutions have y parametrized by some power sums from a finite set. This is a continuation of the work of Corvaja and Zannier [4–6] and of the authors [10, 18] on such problems.Mathematics Subject Classification (2000):11D45,11D61Revised version: 6 May 2004     

Quasi-one-dimensional K-O chain in PTCDA thin films: evidence from first-principles calculations

Using density functional theory calculations we have found that K atoms in a PTCDA (3,4:9,10-perylenetetracarboxylic dianhydride) crystal form a quasi-one-dimensional (1D) K-O chain interacting with carboxylic oxygen of the terminal anhydride groups of PTCDA. The K-K distance in the chain (3.72 Angstrom) is commensurate to the periodicity of the organic semiconductor. We obtain that the K-O structure is stabilized by charge transfer from K to PTCDA molecules, forming prevalently ionic bonds: the electronic density of the chemistry induced gap states is essentially delocalized on the perylene core of PTCDA, while potassium appears spoiled of its charge. Band dispersion along the direction of molecular stack is evaluated to be 0.2 eV in pure PTCDA crystal and 0.5 eV in the K-doped system, confirming that the interaction occurs between different molecular planes.     

The oxidation potential of adenosine and adenosine-thymidine base pair in chloroform solution

The oxidation potential of 2',3'-O-isopropylidene-5'-O-(tert-butyldimethylsilyl)adenosine and its change upon pairing with the complementary base thymidine have been studied in chloroform solution by voltammetric methods. Differential pulse and cyclic voltammetry of an equimolar solution of the two nucleosides show two well-resolved peaks, which have been assigned to the formation of a H-bonded complex between the two nucleosides and to the fraction of unassociated adenosine in solution. No signal for thymidine oxidation has been detected. Equilibrium constants and enthalpy and entropy changes for self- and hetero-association in solution have been determined by NMR spectra. Quantum mechanical computations show that Hoogsteen and Watson-Crick association modes are of comparable stability in solution, and exhibit very similar oxidation potential in chloroform.     

A new route towards redox bistability through the inspection of manganese-porphyrin complexes

The redox and spin versatilities of manganese–porphyrin complexes [Mn^IIP] are examined to construct a redox‐switchable device. The electronic structure of [Mn^IIIP]⁺ was analyzed by using wavefunction‐based calculations (complete active spaces plus single excitations on top of the active spaces, that is, CAS+singles). A non‐negligible σ‐type electron‐transfer configuration is present in the [Mn^IIIP]⁺ S=2 ground state. By contrast, the [Mn^IIP^.]⁺ valence tautomer is a purely π‐type intramolecular charge transfer, thus reflecting an S=3 spin state as a result of the strong ferromagnetic interaction (J=30 meV) between the S=5/2 Mn^II ion and the S=1/2 porphyrin radical cation P^.+. The change of the redox‐sensitive site in the valence tautomer leads to a ‘triangular scheme’ that involves a critical step in which a simultaneous electron transfer and spin change are expected to induce bistability. From the wavefunction inspection, a meso‐substituted porphyrin candidate was designed to support this scenario. The complete active‐space second‐order perturbation theory (CASPT2) adiabatic energy difference between the S=2 and the S=3 spin states was reduced down to 0.15 eV, thereby giving rise to a metastable S=3 state characterized by a 0.10 Å extension of the porphyrin cavity radius. These results not only confirm the rather versatile nature of these inorganic systems but also demonstrate that redox and spin changes are intermingled in this class of compounds and can be used for applied devices.     

Full configuration interaction study of the metal-insulator transition in model systems: LiN linear chains (N=2,4,6,8)

The precursor of the metal-insulator transition is studied at ab initio level in linear chains of equally spaced lithium atoms. In particular, full configuration interaction calculations (up to 1 x 10(9) determinants) are performed, in order to take into account the different nature of the wave function at different internuclear distances. Several indicators of the Metal-Insulator transition (minimum of the energy gap, maximum of the localization tensor or of the polarizability) are considered and discussed. It is shown that the different indicators give concordant results, showing a rapid change in the nature of the wave function at an internuclear distance of about 7 bohrs.     

Fragment-based de novo ligand design by multiobjective evolutionary optimization

GANDI (Genetic Algorithm-based de Novo Design of Inhibitors) is a computational tool for automatic fragment-based design of molecules within a protein binding site of known structure. A genetic algorithm and a tabu search act in concert to join predocked fragments with a user-supplied list of fragments. A novel feature of GANDI is the simultaneous optimization of force field energy and a term enforcing 2D-similarity to known inhibitor(s) or 3D-overlap to known binding mode(s). Scaffold hopping can be promoted by tuning the relative weights of these terms. The performance of GANDI is tested on cyclin-dependent kinase 2 (CDK2) using a library of about 14 000 fragments and the binding mode of a known oxindole inhibitor to bias the design. Top ranking GANDI molecules are involved in one to three hydrogen bonds with the backbone polar groups in the hinge region of CDK2, an interaction pattern observed in potent kinase inhibitors. Notably, a GANDI molecule with very favorable predicted binding affinity shares a 2-N-phenyl-1,3-thiazole-2,4-diamine moiety with a known nanomolar inhibitor of CDK2. Importantly, molecules with a favorable GANDI score are synthetic accessible. In fact, eight of the 1809 molecules designed by GANDI for CDK2 are found in the ZINC database of commercially available compounds which also contains about 600 compounds with identical scaffolds as those in the top ranking GANDI molecules.     

Separation of O- and C-allyl glycoside anomeric mixtures by capillary electrophoresis and high-performance liquid chromatography

Rapid and reliable methods for the analysis of O- and C-allyl galactopyranosides and glucopyranosides are presented, based on capillary zone electrophoresis (CZE) and micellar electrokinetic capillary chromatography (MEKC). In MEKC, the formation of chromophoric and charged complexes between the saccharides and borate as well as the hydrophobic interactions with micelles jointly contributed to the selective separation and sensitive detection of all the investigated anomeric couples. Some non-purified synthesis mixtures of C-allyl glycosides were successfully characterised without pre-treatment. MEKC buffer conditions for which glycosides separation was successfully achieved were then exported and applied to reverse-phase liquid chromatography (RP-HPLC), for the quantitative isolation of each allyl glycoside anomer. Identification of the obtained anomeric products was performed by electrospray mass spectrometry and (13)C NMR spectroscopy. Glycoside-solvent interactions driving the selective anomeric separation were shortly addressed and discussed on the basis of sugar derivatives structural differences.