Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Theoretical study of the absorption and nonradiative deactivation of 1-nitronaphthalene in the low-lying singlet and triplet excited states including methanol and ethanol solvent effects

The photophysics of the 1-nitronaphthalene molecular system, after the absorption transition to the first singlet excited state, is theoretically studied for investigating the ultrafast multiplicity change to the triplet manifold. The consecutive transient absorption spectra experimentally observed in this molecular system are also studied. To identify the electronic states involved in the nonradiative decay, the minimum energy path of the first singlet excited state is obtained using the complete active space self-consistent field//configurational second-order perturbation approach. A near degeneracy region was found between the first singlet and the second triplet excited states with large spin-orbit coupling between them. The intersystem crossing rate was also evaluated. To support the proposed deactivation model the transient absorption spectra observed in the experiments were also considered. For this, computer simulations using sequential quantum mechanic-molecular mechanic methodology was used to consider the solvent effect in the ground and excited states for proper comparison with the experimental results. The absorption transitions from the second triplet excited state in the relaxed geometry permit to describe the transient absorption band experimentally observed around 200 fs after the absorption transition. This indicates that the T-2 electronic state is populated through the intersystem crossing presented here. The two transient absorption bands experimentally observed between 2 and 45 ps after the absorption transition are described here as the T-1 -> T-3 and T-1 -> T-5 transitions, supporting that the intermediate triplet state (T-2) decays by internal conversion to T-1. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4738757]

Dissociative electron attachment to chloromethane.

A low energy electron may attach to a molecule, forming a metastable resonance, which may dissociate into a stable anion and a neutral radical. Chloromethane has been a good target for dissociative electron attachment studies, since it is a small molecule with a clear dissociative ‘sigma*’ shape resonance. We present potential energy curves for CH3Cl and its anion, as a function of the C-Cl distance. Due to the resonant nature of the anion, a correct description requires a treatment based on scattering calculations. In order to compute elastic cross sections and phase shifts we employed the Schwinger multichannel method, implemented with pseudopotentials of Bachelet, Hamann and Schlüter, at the static-exchange plus polarization approximation. At the equilibrium geometry, the resonance was found arround 3.3 eV, in accordance to experience. The incoming electron is captured by a ‘sigma*’ orbital located at the C-Cl bond, which will relax in the presence of this extra electron. We took this bond as the reaction coordinate, and performed several scattering calculations for a series of nuclear conformations. The phase shift obtained in each calculation was fitted by a two component function, consisting in the usual Breit-Wigner profile, which captures the resonant character, and a second order polynomial in the wave number, which accounts for the background contribution. That way, we obtained position and width of the resonance, which allowed us to build the potential energy curve. For larger distances, the anion becomes stable and usual electronic structure calculations suffice. Furthermore, the existence of a dipole-bound anion state is revealed when we employed a set of very diffuse functions. The knowledge on the behaviour of the neutral and anionic electronic states helps us in elucidating how the dissociation takes place.

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.