Uncoupled approach

It is easily realized that the expressions given in Eqs. (6.66) and (6.67) correspond to what is usually termed the uncoupled approach . The argument is simply that there appears no coupling between the different perturbed orbitals that appear in Eq. (6.67). This finding also means that the expression given in Eq. (6.66) can be rewritten in the following sum-over-... 

This is generally true and, for example, is the reason why in the CPHF equations for magnetic perturbations there is only an exchange contribution and no Coulomb contribution due to the perturbed orbitals. The first-order FIF density vanishes, while the first-order HF density matrix is non-zero. In DFT, all contributions (Coulomb, exchange, and correlation) are described via the electron density with the (physically incorrect) consequence that there are no corresponding perturbed contributions in the case of magnetic perturbations. As there is no perturbed contribution, there is no coupUng between the perturbed orbitals and we obtain an uncoupled approach. Computationally, the uncoupled approach is easy to implement, but it needs to be emphasized that it is not correct from a theoretical viewpoint. What are the solutions to the above mentioned problems ... 

The simplest (and perhaps the most popular) solution is to simply ignore the problem. The numerical results obtained in DFT calculations with the uncoupled approach (see Section IV) provide some pragmatic justification for this approach, but of course it is not... 

The alternative approach is to pad the fabric with the alkaline naphthol and dry, foUowed by printing directly onto this prepared fabric diazonium salts or stabilized diazonium salts. Coupling is instant and the only further treatment needed is to remove aU the uncoupled naphthol and surface azo pigment in a subsequent washing treatment. Because the choice of colors is limited from one naphthol component, other shades are obtained by using other classes of dye alongside the azoic colors, eg, reactives. This approach is widely used in the production of African prints. 

As is apparent from the above definitions, each of these effective matrices depend on basis sets and molecular orbitals of both fragments. It is also important to observe that these matrices possess a correct asymptotic behavior as at large interfragment distances they become the usual overlap and Fock matrices of the separate fragments, while the paired secular systems uncouple and converge to the separate Roothaan equations for the single monomers. Finally, as it is usual in a supermolecular approach, the interaction energy is expressed as... 

Ho NFH, PS Burton, RA Conradi, CL Barsuhn. (1995). A biophysical model of passive and polarized active transport processes in Caco-2 cells Approaches to uncoupling apical and basolateral membrane events in the intact cell. J Pharm Sci 84 21-27. 

Molecular mechanics force fields rest on four fundamental principles. The first principle is derived from the Bom-Oppenheimer approximation. Electrons have much lower mass than nuclei and move at much greater velocity. The velocity is sufficiently different that the nuclei can be considered stationary on a relative scale. In effect, the electronic and nuclear motions are uncoupled, and they can be treated separately. Unlike quantum mechanics, which is involved in determining the probability of electron distribution, molecular mechanics focuses instead on the location of the nuclei. Based on both theory and experiment, a set of equations are used to account for the electronic-nuclear attraction, nuclear-nuclear repulsion, and covalent bonding. Electrons are not directly taken into account, but they are considered indirectly or implicitly through the use of potential energy equations. This approach creates a mathematical model of molecular structures which is intuitively clear and readily available for fast computations. The set of equations and constants is defined as the force... 

In the Lagrangian frame, droplet trajectories in the spray may be calculated using Thomas 2-D equations of motion for a sphere 5791 or the simplified forms)154 1561 The gas velocity distribution in the spray can be determined by either numerical modeling or direct experimental measurements. Using the uncoupled solution approach, many CFD software packages or Navier-Stokes solvers can be used to calculate the gas velocity distribution for various process parameters and atomizer geometries/configurations. On the other hand, somesimple expressions for the gas velocity distribution can be derived from... 

Fractional time stepping is widely used in reacting-flow simulations (Boris and Oran 2000) in order to isolate terms in the transport equations so that they can be treated with the most efficient numerical methods. For non-premixed reactions, the fractional-time-stepping approach will yield acceptable accuracy if A t r . Note that since the exact solution to the mixing step is known (see (6.248)), the stiff ODE solver is only needed for (6.249), which, because it can be solved independently for each notional particle, is uncoupled. This fact can be exploited to treat the chemical source term efficiently using chemical lookup tables. 

For isolated molecules a variety of approaches have proved useful in the interpretation of vibrational spectra. Firstly, a species may approximate to a symmetry higher than its actual. In such cases a correlation with-descent in symmetry from — the higher symmetry usually simplifies the interpretation of its spectra. Secondly, local group vibrations, essentially uncoupled from the vibration of other equivalent or near-equivalent groups, may occur. Thirdly, chemically distinct groups may couple... 

As mentioned above, it is common practice to separate a structure into its major components for purposes of simplifying the dynamic analyses. This uncoupled member by member approach approximates the actual dynamic response since dynamic iteration effects between major structural elements are not considered. Resulting calculated dynamic responses, which include deflections and support reactions, may be underestimated or overestimated, depending on the dynamic characteristics of the loading and the structure. This approximation occurs regardless of the solution method used in performing the uncoupled dynamic analyses. 

Some studies on dynamic interaction effects for two degree of freedom systems have been done by Baker 1983 (pp. 415-418). Although these studies were made using a limited range of variables, results indicate that conservative responses can be obtained using uncoupled SDOF system approximations versus a coupled approach. 

The general results of the 3-D models are more-or-less a superposition of the 2-D models discussed above. Furthermore, most of the 3-D models do not show significant changes in the 1-D sandwich in a local region. In other words, a pseudo-3-D approach would be valid in which the 1-D model is run at points in a 2-D mesh wherein both the channel and rib effects can easily be incorporated. Another pseudo-3-D approach is where the 2-D rib models are used and then moved along the channel, similar to the cases of the pseudo-2-D models described above. This latter approach is similar to that by Baker and Darling. In their model, they uncouple the different directions such that there is a 1-D model in the gas channel and multiple 2-D rib models. However, they neither treat the membrane nor have liquid water. In all, the use of CFD means that it is not significantly more complicated to run a complete 3-D model in all domains. 

The aims of this study were to observe isotropically shifted signals for metal ions like copper(II), which usually give signals broadened beyond detection, and to relate the observed shifts and relaxation times to those of the uncoupled ions in order to understand the phenomena in theoretical terms. This approach allows the power of the NMR technique to fully exploit paramagnetic species and obtain information on spin delocalization, chemical bonding and so on. It is likely that the theory also applies to coupled metal ion-H adical systems like those proposed for derivatives of peroxidases (compound I), which contain iron(IV) and a heme radical (44). 

Because rodent populations world-wide were becoming resistant to the widely used Warfarin-type anticoagulant poisons, a search was initiated to find a rodenticide with a different mode of action one that would be effective against these resistant rodents. This search led to the discovery of the toxic nature of a family of diphenyl amines which act as uncouplers of oxidative phosphorylation. A structure-activity relationship (SAR) study was undertaken to choose a derivative that would be both poisonous to rodents but still readily consumed by them. This approach led to the discovery of bromethalin,... 

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