Towards a rigorous treatment of the Jeans-Landau-Teller method for the energy exchanges of harmonic oscillators

For classical Hamiltonian systems containing an harmonic oscillator of high frequency, one has the problem of controlling the energy exchange between the oscillator and the remaining slow degrees of freedom; under very general conditions, such an exchange turns out to be exponentially small with the frequency of the oscillator. In the Jeans-Landau-Teller method, one aims to prove the exponential dependence, and to estimate the coefficient of the exponential, by exploiting the analyticity properties of the solution of the differential equations describing the motion of the system. However, in practice, since the exact solution is not known, such properties are inferred from those of an approximate solution, with no control of the difference; this fact might a priori even invalidate the exponential dependence itself. In the present paper a rigorous treatment is given, for a particular model of interest in the domain of atomic collisions, by keeping control of the difference between the exact and the approximate solution.     

Nickel-Catalyzed Preparations of Functionalized Organozincs

The reaction of primary alkyl bromides or chlorides with diethylzinc in the presence of Ni(acac)(2) (5 mol %) furnishes the corresponding alkylzinc halides (X = Br, Cl) via a halogen-zinc exchange reaction. The treatment of terminal alkenes with diethylzinc (neat, 25-60 degrees C) in the presence of Ni(acac)(2) as a catalyst (1-5 mol %) and 1,5-cyclooctadiene (COD) affords the corresponding dialkylzincs via a hydrozincation reaction. Whereas the conversion for simple alkenes bearing a remote functionality reaches 40 to 63%, the hydrozincation of allylic, homoallylic alcohols and allylic amines proceeds very efficiently (85-95% conversion). All the zinc organometallics obtained react with various electrophiles (allylic halides, enones, acid chlorides, alkynyl halides, ethyl propiolate) after transmetalation with CuCN.2LiCl. In the presence of the chiral catalyst 12, the dialkylzincs prepared add to aldehydes with high enantioselectivity.     

Geminate rebinding in R-state hemoglobin: kinetic and computational evidence for multiple hydrophobic pockets

Biphasic geminate rebinding of CO to myoglobin upon flash photolysis has been associated to ligand distribution in hydrophobic cavities, structurally detected by time-resolved crystallography, xenon occupancy, and molecular simulations. We show that the time course of CO rebinding to human hemoglobin also exhibits a biphasic geminate rebinding when the protein is entrapped in wet nanoporous silica gel. A simple branched kinetic scheme, involving the bound state A, the primary docking site C, and a secondary binding site B was used to calculate the microscopic rates and the time-dependent population of the intermediate species. The activation enthalpies of the associated transitions were determined in the absence and presence of 80% glycerol. Potential hydrophobic docking cavities within the alpha and beta chains of hemoglobin were identified by computational modeling using xenon as a probe. A hydrophobic pocket on the distal side of the heme, corresponding to Xe4 in Mb, and a nearby site that does not have a correspondence in Mb were detected. Neither potential xenon sites on the proximal side nor a migration channel from the distal to proximal site was located. The small enthalpic barriers between states B and C are in very good agreement with the location of the xenon sites on the distal side. Furthermore, the connection between the two xenon sites is relatively open, explaining why the decreased mobility of the protein with viscosity only slightly perturbs the energetics of ligand migration between the two sites.     

Crystal and molecular structure and magnetic exchange properties of bis(di-micro-ethoxo-bis(3,5-di-tert-butylsemiquinonato)dicopper(II)) complex. A synergy between DFT and experimental magnetochemistry

The compound bis(di-micro-ethoxo-bis(3,5-di-tert-butylsemiquinonato)dicopper(II)) has been synthesized and its structure was determined by single-crystal X-ray diffraction. The compound crystallizes in the monoclinic system, space group C2/c, with a = 37.736(8) A, b = 9.173(2) A, c = 23.270(5) A, beta = 122.24(3) degrees. The structure can be described as a Lewis adduct between two dinuclear [Cu(DBSQ)(C(2)H(5)O)](2) units (DBSQ = 3,5-di-tert-butyl-semiquinonato). The temperature dependence of the magnetic susceptibility was efficiently analyzed by a combined DFT/experimental approach, showing that a rather strong ferromagnetic interaction exists between the DBSQ(-) and the copper(II) ions modulated by an antiferromagnetic interaction between the two copper(II) ions of the dinuclear units. Weak antiferromagnetism between the two units in the unit cell was measured.     

Tetraaryl-methane analogues in group 14—V. Distortion of tetrahedral geometryin terms of through-space π–π and π–σ interactions andNMR sagging in terms of π–σcharge transfer

44 members of thecompound series Ph_4−nMR_n (M=Si, Ge, Sn, Pb; R=o-, m-, p-Tol; n=0–4) were synthesized (15 newcompounds). The crystal structures of Ph₃Sn (o-Tol) and PhSn (o-Tol)₃ were determined and compared to 16 known structures. Subject to the distanced (M–C), an interplay between through-space π–π repulsion and π–σ attraction leads to either elongated or compressed tetrahedral geometry. ²⁹ Si-, ¹¹⁹ Sn- and ²⁰⁷ Pb-NMR chemical shifts were determined in solution and in the solid state. ⁷³ Ge chemical shifts were measured only in solution. Anupfield or downfield sagging of the chemical shifts along each series is rationalized in terms of a π–σcharge transfer which is constrained by torsion of the aromatic groups.     

Chemometric studies in the Lagoon of Venice, Italy. Annual evolution of sulphur species and relationship to biogeochemical cycles in lagoon water

During the period March 1997-March 1998 dimethyl sulphide (DMS), dimethylsulphoniopropionate (DMSP) and carbon disulphide (CS2) were determined weekly in the water of the Lagoon of Venice, Italy (at three stations located in the Giudecca Canal, the San Secondo Canal and the Rio di San Nicolò). At the same time, the following hydrological and biological variables were also measured: tide height, temperature, transmittance, fluorescence, pH, salinity, chlorinity, sulphate, ammonia, nitrite, nitrate, phosphate, silicate, chlorophyll a, phaeopigments, phytoplankton (abundance and biomass). Principal component analysis (PCA), applied as a dimension reduction tool, made it possible to summarize multivariate information in a small number of components, which highlighted the relationships between the temporal evolutions of the sulphur compounds with hydrological and biological variables in the seasonal biogeochemical cycle of the lagoon. In particular the overall temporal cycle, which begins with the development of biological activity in late winter and spring, followed by the predominance of degradation processes during the late summer and the remineralization of nutrients in autumn, is clearly described in the plane of the first two principal components, together with the interrelationships between all the relevant variables.     

Formation of dinuclear,macrocyclic, and chain structures from HgI(2) and a semirigid benzimidazole-based bridging ligand: an example of ring-opening supramolecular isomerism

The reactions of HgI(2) with the semirigid ditopic ligand 1,3-bis(benzimidazol-1-ylmethyl)-2,4,6-trimethylbenzene (bbimms) afforded three new complexes, [Hg(2)(mu-I)(2)I(2)(bbimms)] (1), [Hg(2)I(4)(bbimms)(2)] (2), and catena-poly[HgI(2)(bbimms)] (3). The ligand and all complexes have been structurally characterized by single-crystal X-ray diffraction. 1 is a triply bridged dinuclear complex comprised of two Hg(II) ions, one bridging ligand, two bridging I(-) anions, and two terminal I(-) anions. 2 is a dinuclear metallamacrocycle comprised of two Hg(II) ions, two bridging ligands, and four terminal I(-) anions, while 3 is a helical chain with the repeating unit of HgI(2)(bbimms). 2 and 3 can be classified as supramolecular isomers, and both are related to the triply bridged precursor 1 via the addition of one more ligand in a ring-opening process.     

Fluid-like behavior of a one-dimensional granular gas

We study the properties of a one-dimensional (1D) granular gas consisting of N hard rods on a line of length L (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature Tb and viscosity gamma. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature Tg=mv2, kinetic pressure, and density rho=N/L. Thereafter, we consider the fluctuations around the average behavior obtaining a slightly non-Gaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the k approximately 0 region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical subdiffusive behavior of 1D stochastically driven systems, i.e., approximately Dt(1/2), where D for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave vectors.     

Role of secondary structure in the asymmetric acylation reaction catalyzed by peptides based on chiral C alpha-tetrasubstituted alpha-amino acids

In a recent series of papers, Miller and co-workers were able to show that His(pi-Me)-based, terminally protected peptides are potent catalysts of the asymmetric acyl transfer reaction, useful for the kinetic resolution of alcohols. In a structure-supporting solvent, one of the most active compounds, an Aib-containing tetrapeptide, is folded in a doubly intramolecularly H-bonded beta-hairpin motif incorporating a type-II' beta-turn conformation. In this work, we have expanded the study of the Miller tetrapeptide by examining a set of analogues and shorter sequences (dipeptide amides), characterized by chiral C(alpha)-tetrasubstituted alpha-amino acids of diverging bulkiness and optical configuration. Peptide synthesis in solution, conformational analysis by FT-IR absorption and (1)H NMR techniques, and screening of catalytic activity as well have been performed. Our results confirm the close relationship between the beta-hairpin 3D-structure and the catalytic activity of the peptides. A tetrapeptide analogue slightly more selective than the Miller compound has been found. However, the terminally protected, industrially more appealing, dipeptide amides are poorly effective.     

Square Planar (SP-4) and Octahedral (OC-6) Complexes of Platinum(II) and -(IV) with Predetermined Chirality at the Metal Center

cis-Bis-homoleptic platinum(II) complexes, with predetermined helical chirality at the metal center, can be obtained by using strongly sterically interacting ligands. With this aim, two new ligands, (8R,10R)-2-(2'-thienyl)-4,5-pinenopyridine, th4,5ppy (2), and (8R,10R)-2-(2'-thienyl)-5,6-pinenopyridine, th5,6ppy (4), were synthesized and coordinated to platinum. The structures of the resulting complexes, Pt(th4,5ppy)(2) (5) and Pt(th5,6ppy)(2) (6), were determined by X-ray diffraction, and it was found that they both crystallize with a Delta-cis configuration. Thermal oxidative additions (TOA) of alkyl halides were performed with both complexes leading, in the case of 5, to a mixture of isomers and, in the case of 6, to isomerically pure products. The predetermination of chirality at the metal center is therefore preserved in the octahedral (OC-6) platinum(IV) complexes. Crystals of Pt(th4,5ppy)(2) (5) are orthorhombic, of space group P2(1)2(1)2(1), with a = 12.973(1) ?, b = 13.619(2) ?, c = 17.665(2) ?, alpha = beta = gamma = 90 degrees, and Z = 4. Final R = 0.0268 and R(w) = 0.0424 for 3101 observed reflections. Crystals of Pt(th5,6ppy)(2) (6) are hexagonal, of space group P6(1), with a = 11.5465(4) ?, b = 11.5465(4) ?, c = 35.356(3) ?, alpha = beta = 90 degrees, gamma = 120 degrees, and Z = 6. Final R = 0.0424 and R(w) = 0.0845 for 2660 observed reflections. Neither molecule possesses a crystallographic C(2) symmetry.