Accurate ab initio potential energy surfaces for the (3)A '' and (3)A ' electronic states of the O(P-3) plus HBr system

In this work, we report the construction of potential energy surfaces for the (3)A '' and (3)A' states of the system O(P-3) + HBr. These surfaces are based on extensive ab initio calculations employing the MRCI+Q/CBS+SO level of theory. The complete basis set energies were estimated from extrapolation of MRCI+Q/aug-cc-VnZ(-PP) (n = Q, 5) results and corrections due to spin-orbit effects obtained at the CASSCF/aug-cc-pVTZ(-PP) level of theory. These energies, calculated over a region of the configuration space relevant to the study of the reaction O(P-3) + HBr -> OH + Br, were used to generate functions based on the many-body expansion. The three-body potentials were interpolated using the reproducing kernel Hilbert space method. The resulting surface for the (3)A '' electronic state contains van der Waals minima on the entrance and exit channels and a transition state 6.55 kcal/mol higher than the reactants. This barrier height was then scaled to reproduce the value of 5.01 kcal/mol, which was estimated from coupled cluster benchmark calculations performed to include high-order and core-valence correlation, as well as scalar relativistic effects. The (3)A' surface was also scaled, based on the fact that in the collinear saddle point geometry these two electronic states are degenerate. The vibrationally adiabatic barrier heights are 3.44 kcal/mol for the (3)A '' and 4.16 kcal/mol for the (3)A' state. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705428]

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Conditions for the validity of the quantum Langevin equation

From microscopic models, a Langevin equation can, in general, be derived only as an approximation. Two possible conditions to validate this approximation are studied. One is, for a linear Langevin equation, that the frequency of the Fourier transform should be close to the natural frequency of the system. The other is by the assumption of "slow" variables. We test this method by comparison with an exactly soluble model and point out its limitations. We base our discussion on two approaches. The first is a direct, elementary treatment of Senitzky. The second is via a generalized Langevin equation as an intermediate step.

An environmentally friendly analytical procedure for nickel determination by atomic and molecular spectrometry after cloud point extraction in different samples

Cloud point extraction (CPE) was employed for separation and preconcentration prior to the determination of nickel by graphite furnace atomic absorption spectrometry (GFAAS), flame atomic absorption spectrometry (FAAS) or UV-Vis spectrophotometry. Di-2-pyridyl ketone salicyloylhydrazone (DPKSH) was used for the first time as a complexing agent in CPE. The nickel complex was extracted from the aqueous phase using the Triton X-114 surfactant. Under optimized conditions, limits of detection obtained with GFAAS, FAAS and UV-Vis spectrophotometry were 0.14, 0.76 and 1.5 mu g L-1, respectively. The extraction was quantitative and the enrichment factor was estimated to be 27. The method was applied to natural waters, hemodialysis concentrates, urine and honey samples. Accuracy was evaluated by analysis of the NIST 1643e Water standard reference material.

Stability boundary characterization of nonlinear autonomous dynamical systems in the presence of saddle-node equilibrium points

A dynamical characterization of the stability boundary for a fairly large class of nonlinear autonomous dynamical systems is developed in this paper. This characterization generalizes the existing results by allowing the existence of saddle-node equilibrium points on the stability boundary. The stability boundary of an asymptotically stable equilibrium point is shown to consist of the stable manifolds of the hyperbolic equilibrium points on the stability boundary and the stable, stable center and center manifolds of the saddle-node equilibrium points on the stability boundary.