Double description

The basis sets were chosen to be of a rather limited size, especially for the metal atom, because a more limited basis set might enable the use of larger aggregates of atoms at acceptable cost. Therefore, the /7 CMJo-potentials approximation for the inner electrons together with the minimum basis set for description of the valence electrons, known as the LANLIMB basis set, was favored, but a double- description of the valence electrons, LANLIDZ, was also tested. For halide ions the valence electrons were always described with double-C quality basis set and for the three larger ions the core p enJo-potentials were applied.The nomenclature MB-DZ and DZ-DZ, used in subsequent discussion, refers then to the LANLIMB or LANLIDZ basis set used for the Cu atom combined with the LANLIDZ basis set used for the halide ion. Because the final goal of the work was to use the metal cluster model, these tests enabled us to select the combination of basis sets and method that will compensate for the loss of quality arising from the limitations which result from the size of the basis set used for the metal atoms. 

One very fast EFM enumeration method uses the binary nullspace implementation [20, 21] of the double description (DD) method [22]. This method has proven particularly useful for the complete enumeration of EFMs in metabolic networks [22]. 

Fukuda, K. and Prodon, A. (1996) Double description method revisited, in Combinatorics and Computer Science, Lecture Notes in Computer Science, Vol. 1120, Springer-Verlag, Berlin Heidelberg, pp. 91-111. 

A disadvantage of a manual for each department is, when multiple departments of the same (pharmacy) organisation are described in this way, this usually leads to double descriptions and indistinctness about relationships between departments. 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

In this section, the adiabatic picture will be extended to include the non-adiabatic terais that couple the states. After this has been done, a diabatic picture will be developed that enables the basic topology of the coupled surfaces to be investigated. Of particular interest are the intersection regions, which may form what are called conical intersections. These are a multimode phenomena, that is, they do not occur in ID systems, and the name comes from their shape— in a special 2D space it has the fomi of a double cone. Finally, a model Flamiltonian will be introduced that can describe the coupled surfaces. This enables a global description of the surfaces, and gives both insight and predictive power to the fomration of conical intersections. More detailed review on conical intersections and their properties can be found in [1,14,65,176-178]. 

Fig. 1. Structure adapted hierarchical description of Coulomb interactions in biological macromolecules. Filled circles (level 0) represent atoms, structural units (li vel 1) are surrounded by a single-line border, and clusters (level 2) are surrounded by a double-line border.

Because the carbons that are singly bonded m one resonance form are doubly bonded m the other the resonance description is consistent with the observed carbon-carbon bond distances m benzene These distances not only are all identical but also are intermediate between typical single bond and double bond lengths... 

The General References and two other reviews (17,25) provide extensive descriptions of the chemistry of maleic anhydride and its derivatives. The broad industrial appHcations for this chemistry derive from the reactivity of the double bond in conjugation with the two carbonyl oxygens. 

In electrode kinetics a relationship is sought between the current density and the composition of the electrolyte, surface overpotential, and the electrode material. This microscopic description of the double layer indicates how stmcture and chemistry affect the rate of charge-transfer reactions. Generally in electrode kinetics the double layer is regarded as part of the interface, and a macroscopic relationship is sought. For the general reaction... 

The hybridization concept can also be applied to molecules containing double and triple bonds. The descriptive valence bond approach to the bonding in ethylene and... 

HaO). Quinine salicylate, 2[B. CgH4(OH)(COOH)]. HaO, forms colourless needles, m.p. 187° (dec.), which slowly become pink in air. It is soluble in water (1 in 77 at 25°), alcohol (1 in 11 at 25°), or chloroform (1 in 37 at 25°). The foregoing are the most important quinine salts used in medicine, but many other salts have been used, e.g., the tannate, formate, valerate, ethylcarbonate, lactate, cacodylate, etc., as well as double salts such as quinine bismuth iodide. Descriptions of many of these salts will be found in the British Pharmaceutical Codex for 1934. 

In some cases, e.g., the Hg/NaF q interface, Q is charge dependent but concentration independent. Then it is said that there is no specific ionic adsorption. In order to interpret the charge dependence of Q a standard explanation consists in assuming that Q is related to the existence of a solvent monolayer in contact with the wall [16]. From a theoretical point of view this monolayer is postulated as a subsystem coupled with the metal and the solution via electrostatic and non-electrostatic interactions. The specific shape of Q versus a results from the competition between these interactions and the interactions between solvent molecules in the mono-layer. This description of the electrical double layer has been revisited by... 

The first basic ingredient in our description of the electric double layer is the coulombic interaction. It seems quite natural to assume that the fields are coupled according to a coulombic Hamiltonian of the same... 

Z. Borkowska, J. Stafiej, J. P. Badiah. Simple description of ionic solution at electrified interfaces. Proceedings of the Symposium on the Electrochemical Double Layer, Montreal, 1997, pp. 120-130. 

In both cases, the double excitation Ag state is lower in energy than the singe excitation state. However, the energy difference continuously decreases as the CAS description is improved. Adding an MP2 correction would decrease it even further. 

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