An experimental and theoretical investigation of gas-phase reactions of Ca2+ with glycine

The gas-phase reactions between Ca(2+) and glycine ([Ca(gly)](2+)) have been investigated through the use of mass spectrometry techniques and B3-LYP/cc-pWCVTZ density functional theory computations. The major peaks observed in the electrospray MS/MS spectrum of [Ca(gly)](2+) correspond to the formation of the [Ca,C,O(2),H](+), NH(2)CH(2) (+), CaOH(+), and NH(2)CH(2)CO(+) fragment ions, which are produced in Coulomb explosion processes. The computed potential energy surface (PES) shows that not only are these species the most stable product ions from a thermodynamic point of view, but they may be produced with barriers lower than for competing processes. Carbon monoxide is a secondary product, derived from the unimolecular decomposition of some of the primary ions formed in the Coulomb explosions. In contrast to what is found for the reactions of Ca(2+) with urea ([Ca(urea)](2+)), minimal unimolecular losses of neutral fragments are observed for the gas-phase fragmentation processes of [Ca(gly)](2+), which is readily explained in terms of the topological differences between their respective PESs.     

Rayleigh–Schrödinger series and Birkhoff decomposition

We derive new expressions for the Rayleigh–Schrödinger series describing the perturbation of eigenvalues of quantum Hamiltonians. The method, somehow close to the so-called dimensional renormalization in quantum field theory, involves the Birkhoff decomposition of some Laurent series built up out of explicit fully non-resonant terms present in the usual expression of the Rayleigh–Schrödinger series. Our results provide new combinatorial formulae and a new way of deriving perturbation series in quantum mechanics. More generally we prove that such a decomposition provides solutions of general normal form problems in Lie algebras.     

Topological approach to solve frame structures using topological collections and transformations

The present work tackled the modeling of frame structures using a topological approach based on the concepts of topological collections and transformations. The topological collections are used to specify the interconnection law between the frame structures and the transformations that are used to describe their behavior. As a language allowing the application of this approach, we applied the MGS (Modeling of General System) language. To validate this approach, we studied the case of two- and three-dimensional frame structures. Then, the results obtained using the MGS language are presented and compared to those obtained by the structural calculation software by the finite-element method RDM6. For both studied cases, we find that the results obtained by MGS language based on the notions of topological collections and transformations and those obtained by the RDM6 software based on the finite element method are very close, which validates our approach. Using this topological approach, any structure can be characterized by local relations between its elements, thus making it possible to dissociate its topology and its physics. Indeed, in our topological approach, we separately define the topology of the studied frame structure and the local behavior law as well as the equilibrium equations of its various components. Therefore, this topological approach might be generalized to model complex systems which can be considered as a set of local elements linked by a neighborhood relationship.     

Collision induced dissociation of doubly-charged ions: Coulomb explosion vs. neutral loss in [Ca(urea)](2+) gas phase unimolecular reactivity via chemical dynamics simulations

In this paper we report different theoretical approaches to study the gas-phase unimolecular dissociation of the doubly-charged cation [Ca(urea)](2+), in order to rationalize recent experimental findings. Quantum mechanical plus molecular mechanical (QM/MM) direct chemical dynamics simulations were used to investigate collision induced dissociation (CID) and rotational-vibrational energy transfer for Ar + [Ca(urea)](2+) collisions. For the picosecond time-domain of the simulations, both neutral loss and Coulomb explosion reactions were found and the differences in their mechanisms elucidated. The loss of neutral urea subsequent to collision with Ar occurs via a shattering mechanism, while the formation of two singly-charged cations follows statistical (or almost statistical) dynamics. Vibrational-rotational energy transfer efficiencies obtained for trajectories that do not dissociate during the trajectory integration were used in conjunction with RRKM rate constants to approximate dissociation pathways assuming complete intramolecular vibrational energy redistribution (IVR) and statistical dynamics. This statistical limit predicts, as expected, that at long time the most stable species on the potential energy surface (PES) dominate. These results, coupled with experimental CID from which both neutral loss and Coulomb explosion products were obtained, show that the gas phase dissociation of this ion occurs by multiple mechanisms leading to different products and that reactivity on the complicated PES is dynamically complex.     

Electrochemical coupling of mono and dihalopyridines catalyzed by nickel complex in undivided cell

One step nickel-catalyzed electroreductive homocoupling among 2-bromopicolines and 2-bromopyridine has been investigated by our group in an undivided cell and using zinc or iron as sacrificial anode. In this work, it was developed mono and dihalopyridines coupling to obtain possible products from heterocoupling. A series of reactions were carried out in order to develop a synthetic method for the preparation of unsymmetrical 2,2′-bipyridines and 2,2′:6′,2″-terpyridines. Statistical yields (50%) were observed for 2-bromopyridines/2-bromo-6-methylpyridine heterocoupling. In a preliminary study devoted to terpyridines preparation, good results were obtained for 2,6-dihalopyridines homocoupling, affording 2,6-dichloro-2,2′-bipyridine (46%) and 2,6-dibromo-2,2′-bipyridine (56%), at controlled reaction time. At major reaction time, it was observed that the direct electroreduction of the 2,6′-dihalo-2,2′-bipyridines intermediates and 2,6″-dihalo-2,2′:6′,2″-terpyridines products on the cathode surface. A reasonable isolated product yield of 6,6″-dimethyl-2,2′:6′,2″-terpyridine (10%) was only observed in the reaction between 2,6-dichloropyridine and 2-bromo-6-methylpyridine (1:2).     

Structural Diversity Within the Series of 68-Electron M4L n E2 (L = 2-Electron Ligand; M = Fe, Ru, Os, Co; E = CH, N, P, NR, PR, S) Organometallic Clusters: A Theoretical Investigation

Four different skeletal structural arrangements with very different connectivities are known for 6-vertex/68-electron of M₄E₂ core (M = transition metal; E = main-group atom or ligand). DFT calculations on a large number of title model compounds allow to rationalize the preferences between these structural shapes with respect to the nature of the metal and main-group elements constituting the cluster cage. In particular, the electronegativity of M and the “size” (first-row vs. second-row element) of E play an important role in the stability preference of a particular isomer. For several compounds, although only one type of structure is known, other low-energy isomeric forms are also likely to exist. Moreover, two structural types, so far unreported, are predicted to be stable enough for being synthesized.     

Kraichnan Flow in a Square: An Example of Integrable Chaos

The Kraichnan flow provides an example of a random dynamical system accessible to an exact analysis. We study the evolution of the infinitesimal separation between two Lagrangian trajectories of the flow. Its long-time asymptotics is reflected in the large deviation regime of the statistics of stretching exponents. Whereas in the flow that is isotropic at small scales the distribution of such multiplicative large deviations is Gaussian, this does not have to be the case in the presence of an anisotropy. We analyze in detail the flow in a two-dimensional periodic square where the anisotropy generally persists at small scales. The calculation of the large deviation rate function of the stretching exponents reduces in this case to the study of the ground state energy of an integrable periodic Schrödinger operator of the Lamé type. The underlying integrability permits to explicitly exhibit the non-Gaussianity of the multiplicative large deviations and to analyze the time-scales at which the large deviation regime sets in. In particular, we indicate how the divergence of some of those time scales when the two Lyapunov exponents become close allows a discontinuity of the large deviation rate function in the parameters of the flow. The analysis of the two-dimensional anisotropic flow permits to identify the general scenario for the appearance of multiplicative large deviations together with the restrictions on its applicability.     

A Tabu Search with Slope Scaling for the Multicommodity Capacitated Location Problem with Balancing Requirements

In this paper, a tabu search heuristic is combined with slope scaling to solve a discrete depot location problem, known as the multicommodity location problem with balancing requirements. Although the uncapacitated version of this problem has already been addressed in the literature, this is not the case for the more challenging capacitated version, where each depot has a fixed and finite capacity. The slope scaling approach is used during the initialization phase to provide the tabu search with good starting solutions. Numerical results are reported on various types of large-scale randomly generated instances. The quality of the heuristic is assessed by comparing the solutions obtained with those of a commercial mixed-integer programming code.