Confined model systems problem

Certainly, novel numerical methods [115-120] have to be further developed to treat the confined model systems which include multiple electrons and/or atoms under a wider variety of boundary conditions and symmetry. While confined systems present many computational problems not found in free systems, systems prepared under controlled confinement will continue to have their own virtues. 

In this cavity model the atom is confined at the centre of a spherical box, of finite radius R, with an impenetrable wall. This is, of course, a highly idealised model and its limitations were clearly recognised [3]. However, as pointed out in Fowler s extensive work on confined 1-electron problems [6], it does serve as a framework for discussing properties of localised systems. 

The investigation of the interaction between water and such interfaces is relevant to the study of such problems as the behavior of water in living organisms [4,5] and sludge dewatering [6], Moreover, water enclosed in very small volumes plays a dominant role as the medium that contfols structure and behavior near biological membranes, for example, and microemulsions may weU serve as model systems for the study of water in confined spaces [2,7,8],... 

From the theoretical point of view, a density functional type theory for systems confined to microporous media is lacking. This seems to be one of the reasons why the problem of crystallization of fluids in disordered media has not been solved so far. Further work in future is needed, however, to solve this and relevant problems. Our expectation is that a combined application of theoretical methods and simulation would provide faster progress in studies of fluids and mixtures in microporous media. At present, the models studied in theory and simulations are quite far from the systems of experimental focus. Hopefully, favorable changes will occur in future. 

The present paper has focused on novel systems, doped fullerenes, with the emphasis on their photoionization spectra. While the photoionization problem of gas phase doped fullerenes has been experimentally addressed only recently in pioneering works [12,13], there has been much more activity on the theoretical side of the problem this has far outstripped experiment. In the present paper, only those results obtained on the basis of simple semiem-pirical models, the A-potential [15,20-22,27-33,43,44] and 5-potential [34-41] models have been highlighted. Surprisingly, even within the framework of these simple models a rich variety of novel effects, particularly the confinement resonances and their manifestations in the photoionization spectra of doped fullerenes has been unraveled. Although the approximations made are indisputably reasonable for trusting the existence of, and trends in, the predicted confinement resonances, and thereby urging their experimental... 

In order to keep the formulation as simple as possible we confine the discussion to systems with only two degrees of freedom. The extension to more complex problems is — formally at least — straightforward. We will treat triatomic molecules ABC dissociating into products A+BC. First, we again consider in Section 3.1 the linear model, outlined in Sections 2.4 and 2.5, in which the diatomic fragment vibrates while its rotational degree of freedom is frozen. Subsequently, we treat in Section 3.2 the... 

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