Confined atoms model

In this work, we use the confined atoms model, with hard walls, to estimate the pressure on confined Ca, Sr, and Ba atoms. With this approach, we will give an upper limit to the pressure, because it is well known that the Dirichlet boundary conditions give an overestimation to this quantity. By using this approach, we obtain the profiles of some electronic properties... 

Pressure Effects on the Electronic Properties of Ca, Sr, and Ba by the Confined Atoms Model... 

Table 1 Transition pressures for Ca, Sr and Ba estimated by the confined atom model. Pressure in GPa and...

Before starting the discussion on confined atoms, we shall briefly describe the simplest standard confined quantum mechanical system in three dimensions (3-D), namely the particle-in-a-(spherical)-box (PIAB) model [1], The analysis of this system is useful in order to understand the main characteristics of a confined system. Let us note that all other spherically confined systems with impenetrable walls located at a certain radius, Rc, transform into the PIAB model in the limit of Rc —> 0. For the sake of simplicity, we present the model in one-dimension (1-D). In atomic units (a.u.) (me=l, qc 1, and h = 1), the Schrodinger equation for an electron confined in one-dimensional box is... 

The role of instabilities involving confined impurity atoms has been investigated by Mtiser using a model in which two one-dimensional (1-D) or 2-D surfaces were separated by a very low concentration of confined atoms and slid past one another.25 The motion of the confined atoms was simulated with Langevin dynamics where the interactions between these atoms were neglected and the atom-wall interactions were described by... 

Since the 5-potential model assumes that the size ra of the confined atom is much smaller than the size Rc of the fullerene cage, ra << Rc, only... 

Yoon, Smith, and Matsuda, on the other hand, compared two approaches, using a united-atom model and a fully atomistic model.Stochastic dynamics and MD simulations of w-tridecane (C13H28) were used to study polyethylene. Besides studying the bulk melt, the authors examined confined melts between solid surfaces. Chain conformations, chain packing orientational correlations, and self-diffusion were among the properties studied. In regard to chain confer-... 

Physical properties of atoms and ions in intense magnetic fields are hence obtained in the statistical limit of Thomas-Fermi theory. This discussion is then supplemented by the hyperstrong limit, considered especially by Lieb and co-workers. Chemistry in intense magnetic fields is thereby compared and contrasted with terrestrial chemistry. Some emphasis is then placed on a model of confined atoms in intense electric fields the statistical Thomas-Fermi approximation again being the central tool employed. 

Model of Confined Atoms in Arbitrary Static Electric Field. 80... 

A model of confined atoms in an arbitrary static electric field, which can also be solved analytically, will then be discussed in some detail. Contact will be made with results on atomic ions in non-degenerate plasmas, with illustrative examples being presented. A brief treatment follows of the time-dependent uniform electric field Feynman propagator. 

The independent work of Michels et al. [11] at the end of 1937 considered the hydrogen atom in an impenetrable sphere as a physical model for hydrogen under high pressure and studied the effects of confinement on the polarizability of hydrogen. Usually this paper is referred to as the first work on the confined atom problem, where the Dirichlet boundary conditions were used for quantum-mechanical problems. This work was followed by the work of Sommerfeld et al. [12,13] with the introduction of confluent... 

Nevertheless, important progress can still be made by introducing some refinements and improvements on existing models, which would lead us to a better understanding and a deeper insight into the electronic structure of confined atoms. New experimental results will undoubtedly guide us in the countless tasks that must be performed in the near future. 

Much of the recent work on confined atoms has focussed on the possibility of deriving exact (analytical) solutions, less on the physical origin of the confinement process itself, and we will follow this course here. Our justification is the belief that a model problem amenable to analytical solution is of general interest per se, as it is expected to furnish a good zero-order model for some truly physical system. 

More recently, there has been renewed interest in confined atomic systems in several areas of research for reviews and references see Jaskolski [7], Sako and Diercksen [8,9] and Dolmatov et al. [10], as well as papers here in the present volume. In addition to the spherical box model, the hydrogen atom has also been studied under various types of confinement (see, for example, Ley-Koo and Rubinstein [4], Froman et al. [5], Connerade et al. [11] and Saha et al. [12]), and off-centre investigations of the spherical cavity model have been performed as well [13]. 

One way of limiting the conformational space available to a protein is to confine a model polypeptide to a lattice. In doing so, unrealistic distortions are imposed on protein structure. However, lattice models offer the possibility to enumerate the entire conformational space available to a polymer chain. A detailed atomic picture is not typically employed with lattice models. However, a variety of lattices of increasing complexity facilitate more detailed chain representations, A trade-off exists between the detail of the models and the ability to evaluate conformational alternatives exhaustively. 

The confined atom can be regarded as a first step towards modelling solids, and the problem is of current interest now that numerical methods allow more complex atoms to be studied [35]. It is also a first step towards studying the compressibility of atoms, and their ability to partake in soft chemistry (see section 11.8) [36]. 

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